Carl Pomerance

Phone: (603) 646-2635
Dept. Fax: (603) 646-1312
Office: 339 Kemeny Hall
Office Hours: Tuesday, Wednesday, Thursday
9:00 - 9:55 AM 
Email: carl.pomerance@dartmouth.edu
US Mail: Department of Mathematics
Dartmouth College
Hanover, NH 03755-3551
(603) 646-2415

Brief CV


Books

  1. Lecture Notes on Primality Testing and Factoring: A Short Course at Kent State University, C. Pomerance, MAA Notes 4, Washington, DC, 1984.

  2. Advances in Cryptology: Crypto '87, C. Pomerance, ed., Lecture Notes in Computer Science 293, Springer-Verlag, Berlin, 1988.

  3. Cryptology and computational number theory, C. Pomerance, ed. Proc. Symp. Appl. Math. 42, Amer. Math. Soc., Providence, 1990.

  4. Prime numbers: a computational perspective, R. Crandall and C. Pomerance, Springer-Verlag, New York, 2001.

  5. Prime Numbers: a computational perspective, second edition, R. E. Crandall and C. Pomerance, Springer, New York, 2005. Errata.

  6. Topics in combinatorial number theory: Proceedings of the INTEGERS Conference 2003 in honor of Tom Brown, B. Landman, M. Nathanson, J. Nesetril, and C. Pomerance, eds., DIMATIA, Prague, 2005.

  7. Combinatorial Number Theory: Proceedings of the Integers Conference 2005 in Celebration of the 70th Birthday of Ron Graham, B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, and C. Pomerance, eds., De Gruyter, Berlin, 2007.


Some Talks

  1. Covering talk, Talk on covering congruences (Joint Math Meetings, San Diego, January 2008).

  2. Undergrad covering talk, More elementary talk on covering congruences (Spuyten Duyvil Undergraduate Mathematics Meeting, New York City, April, 2008; Ohio and Michigan MAA Sections, Spring 2008).

  3. Talk on Euler's function, Talk at University of Georgia, February 2008 and Trinity University, March 2008.

  4. Elementary primality talk, Lucas Lecture at Fibonacci Association Meeting in Patras, Greece, July 2008.

  5. Fields talk, Counting Fields. At Canadian Number Theory Association Meeting in Waterloo, Canada, July 2008.

  6. Multiplicative order talk, The multiplicative order mod n, on average. At the Quebec/Maine number theory conference at Laval University, Quebec, Canada, October, 2008.

Papers

  1. Odd perfect numbers are divisible by at least seven distinct primes, C. Pomerance, Acta Arith. 25 (1974), 265-300.

  2. On Carmichael's conjecture, C. Pomerance, Proc. Amer. Math. Soc. 43 (1974), 297-298.

  3. A search for elliptic curves with large rank, D.E. Penney and C. Pomerance, Math. Comp. 28 (1974), 851-853.

  4. 714 and 715, C. Nelson, D.E. Penney, and C. Pomerance, J. Rec. Math. 7 (1974), 87-89.

  5. Three elliptic curves with rank at least seven, D.E. Penney and C. Pomerance, Math. Comp. 29 (1975), 965-967.

  6. The second largest prime factor of an odd perfect number, C. Pomerance, Math. Comp. 29 (1975), 914-921.

  7. On the congruences σ(n) ≡ a (mod n) and n ≡ a (mod φ(n)), C. Pomerance, Acta Arith. 26 (1975), 265-272.

  8. On an interesting property of 112359550561797752809, J.L. Hunsucker and C. Pomerance, Fibonacci Quarterly 13 (1975), 331-333.

  9. There are no odd super perfect numbers less than 7 x 1024, J.L. Hunsucker and C. Pomerance, Indian J. Math. 17 (1975), 107-120.

  10. Some new results on odd perfect numbers, G.G. Dandapat, J.L. Hunsucker, and C. Pomerance, Pacific J. Math. 57 (1975), 359-364.

  11. On multiply perfect numbers with a special property, C. Pomerance, Pacific J. Math. 57 (1975), 511-517.

  12. On composite n for which φ(n)|n-1, I, C. Pomerance, Acta Arith. 28 (1976), 387-389.

  13. Multiply perfect numbers, Mersenne primes and effective computability, C. Pomerance, Math. Ann. 226 (1977), 195-206.

  14. On a tiling problem of R. B. Eggleton, C. Pomerance, Discrete Math. 18 (1977), 63-70.

  15. On composite n for which φ(n)|n-1, II, C. Pomerance, Pacific J. Math. 69 (1977), 177-186.

  16. On the distribution of amicable numbers, C. Pomerance, J. reine angew. Math. 293/294 (1977), 217-222.

  17. On the largest prime factors of n and n+1, P. Erdős and C. Pomerance, Aequationes Math. 17 (1978), 311-321.

  18. On a class of relatively prime sequences, P. Erdős, D.E. Penney, and C. Pomerance, J. Number Theory 10 (1978), 451-474.

  19. The prime number graph, C. Pomerance, Math. Comp. 33 (1979), 399-408.

  20. On a problem of Evelyn - Linfoot and Page in additive number theory, C. Pomerance and D. Suryanarayana, Publ. Math. Debrecen 26 (1979), 237-244.

  21. Nearly parallel vectors, H.G. Diamond and C. Pomerance, Mathematika 26 (1979), 258-268.

  22. Some number theoretic matching problems, C. Pomerance, Proceedings of the Queen's Number Theory Conference, P. Ribenboim, ed., Queen's Papers in Pure and Applied Mathematics, No. 54, Kingston, Canada, 1979, 237-247.

  23. Collinear subsets of lattice point sequences - an analogue of Szemerédi's theorem, C. Pomerance, J. Combinatorial Theory (A) 28 (1980), 140-149.

  24. A note on the least prime in an arithmetic progression, C. Pomerance, J. Number Theory 12 (1980), 218-223.

  25. The pseudoprimes to 25 x 109, C. Pomerance, J.L. Selfridge, and S.S. Wagstaff, Jr., Math. Comp. 35 (1980), 1003-1026.

  26. Matching the natural numbers up to n with distinct multiples in another interval, P. Erdős and C. Pomerance, Nederl. Akad. Wetensch. Proc. Ser. A 83 (1980), 147-161.

  27. Proof of D.J. Newman's coprime mapping conjecture, C. Pomerance and J.L. Selfridge, Mathematika 27 (1980), 69-83.

  28. Popular values of Euler's function, C. Pomerance, Mathematika 27 (1980), 84-89.

  29. Sets on which an entire function is determined by its range, H.G. Diamond, C. Pomerance and L. Rubel, Math. Z. 176 (1981), 383-398.

  30. On the distribution of amicable numbers, II, C. Pomerance, J. reine angew. Math. 325 (1981), 183-188.

  31. The arithmetic mean of the divisors of an integer, P.T. Bateman, P. Erdős, C. Pomerance and E.G. Straus, Analytic Number Theory Proceedings, Philadelphia 1980, M. I. Knopp, ed., Lecture Notes in Math. 899 (1981), 197-220.

  32. On the distribution of pseudoprimes, C. Pomerance, Math. Comp. 37 (1981), 587-593.

  33. Recent results in primality testing, C. Pomerance, Math. Intelligencer 3 (1981), 97-105.

  34. A new lower bound for the pseudoprime counting function, C. Pomerance, Illinois J. Math. 26 (1982), 4-9.

  35. The search for prime numbers, C. Pomerance, Scientific American 247, No. 6 (1982), 136-144.

  36. Analysis and comparison of some integer factoring algorithms, C. Pomerance, Computational Methods in Number Theory, Part I, H.W. Lenstra, Jr. and R. Tijdeman, eds., Math. Centre Tract 154, Amsterdam, 1982, 89-139.

  37. On distinguishing prime numbers from composite numbers, L.M. Adleman, C. Pomerance and R.S. Rumely, Annals Math. 117 (1983), 173-206.

  38. An analogue of Grimm's problem of finding distinct prime factors of consecutive integers, P. Erdős and C. Pomerance, Utilitas Math. 24 (1983), 45-65.

  39. On a problem of Oppenheim concerning `Factorisatio Numerorum', E.R. Canfield, P. Erdős and C. Pomerance, J. Number Theory 17 (1983), 1-28.

  40. Implementation of the continued fraction integer factoring algorithm, C. Pomerance and S.S. Wagstaff, Jr., Congressus Numerantium 37 (1983), 99-117.

  41. On the longest simple path in the divisor graph, C. Pomerance, Proc. Southeastern Conf. Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1983, Cong. Num. 40 (1983), 291-304.

  42. Moduli r for which there are many small primes congruent to a modulo r, P.T. Bateman and C. Pomerance, Publ. Math. d'Orsay 83.04 (1983), 8-19.

  43. Lecture notes on primality testing and factoring - A short course at Kent State University, C. Pomerance, (based on notes by S. M. Gagola, Jr.), MAA Notes 4 (1984).

  44. New ideas for factoring large integers, C. Pomerance, J. W. Smith and S. S. Wagstaff, Jr., Advances in Cryptology, Proc. Crypto 83, D. Chaum, ed., Plenum Press, New York, 1984, 81-85.

  45. Estimates for certain sums involving the largest prime factor of an integer, A. Ivic and C. Pomerance, Proc. Colloquium on Number Theory 34 (1981), Topics in Classical Number Theory, North Holland, 1984, 769-789.

  46. On the size of the coefficients of the cyclotomic polynomial, P. T. Bateman, C. Pomerance and R. C. Vaughan, Proc. Colloquium on Number Theory 34 (1981), Topics in Classical Number Theory, North Holland, 1984, 171-202.

  47. View obstruction problems, III, T. W. Cusick and C. Pomerance, J. Number Theory 19 (1984), 131-139.

  48. The normal number of prime factors of φ(n), P. Erdős and C. Pomerance, Rocky Mtn. J. Math. 15 (1985), 343-352.

  49. On locally repeated values of certain arithmetic functions, I, P. Erdős, C. Pomerance and A. Sárközy, J. Number Theory 21 (1985), 319-332.

  50. Multiplicative relations for sums of initial k-th powers, D.E. Penney and C. Pomerance, Amer. Math. Monthly 92 (1985), 729-731.

  51. On the distribution of round numbers, C. Pomerance, Number Theory Proceedings, Ootacamund, India 1984, K. Alladi, ed., Lecture Notes in Math. 1122 (1985), 173-200.

  52. The quadratic sieve factoring algorithm, C. Pomerance, Advances in Cryptology, Proceedings of Eurocrypt 84, Paris, 1984, T. Beth. N. Cot, and I. Ingemarsson, eds., Lecture Notes in Computer Sci. 209 (1985), 169-182.

  53. On the Schnirelmann and asymptotic densities of certain sets of non-mulitples, P. Erdős, C. B. Lacampagne, C. Pomerance and J. L. Selfridge, Proceedings of the Southeast Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1985, Congressus Numerantium 48 (1985), 67-79.

  54. On sums involving reciprocals of the largest prime factor of an integer, P. Erdős and A. Ivic and C. Pomerance, Glasnik Math. 21 (1986), 283-300.

  55. On the number of false witnesses for a composite number, P. Erdős and C. Pomerance, Math. Comp. 46 (1986), 259-279.

  56. On primitive divisors of Mersenne numbers, C. Pomerance Acta Arith. 46 (1986), 355-367.

  57. On the distribution of the values of Euler's function, C. Pomerance, Acta Arith. 47 (1986), 63-70.

  58. On locally repeated values of certain arithmetic functions, II, P. Erdős, C. Pomerance and A. Sárközy, Acta Math. Hungarica 49 (1987), 251-259.

  59. On the average number of groups of square-free order, C. Pomerance, Proc. Amer. Math. Soc. 99 (1987), 223-231.

  60. The smallest n-uniform hypergraph with positive discrepancy, N. Alon, D. J. Kleitman, C. Pomerance, M. Saks and P. Seymour, Combinatorica 7 (1987), 151-160.

  61. On locally repeated values of certain arithmetic functions, III, P. Erdős, C. Pomerance and A. Sárközy, Proc. Amer. Math. Soc. 101 (1987), 1-7.

  62. Very short primality proofs, C. Pomerance, Math. Comp. 48 (1987), 315-322.

  63. Fast, rigorous factorization and discrete logarithm algorithms, C. Pomerance, Discrete algorithms and complexity, D. S. Johnson, T. Nishizeki, A. Nozaki, H. S. Wilf, eds., Academic Press, Orlando, Florida, 1987, pp. 119-143.

  64. On products of sequences of integers, C. Pomerance and A. Sárközy, Coll. Math. Soc. Janos Bolyai 51 (1987), 447-463.

  65. A pipe-line architecture for factoring large integers with the quadratic sieve algorithm, C. Pomerance, J. W. Smith and R. Tuler, SIAM J. Comput. 17 (1988), 387-403.

  66. On homogeneous multiplicative hybrid problems in number theory, C. Pomerance and A. Sárközy, Acta Arith. 49 (1988), 291-302.

  67. On the number of distinct values of Euler's φ-function, H. Maier and C. Pomerance, Acta Arith. 49 (1988), 263-275.

  68. On divisors of sums of integers, III, C. Pomerance, A. Sárközy and C. L. Stewart, Pacific J. Math. 133 (1988), 363-379.

  69. The generation of random numbers that are probably prime, P. Beauchemin, G. Brassard, C. Crépeau, C. Goutier and C. Pomerance, Journal of Cryptology 1 (1988), 53-64.

  70. Two methods in elementary analytic number theory, C. Pomerance, Number theory and applications, R. A. Mollin, ed., Kluwer Academic Publishers, Dordrecht, 1989, pp. 135-161.

  71. On the composition of the arithmetic functions σ and φ, C. Pomerance, Colloq. Math. 58 (1989), 11-15.

  72. The probability that a random probable prime is composite, S.H. Kim and C. Pomerance, Math. Comp. 53 (1989), 721-741.

  73. Fonction zêta de Riemann et conjecture de Weyl-Berry pour les tambours fractals, M. L. Lapidus and C. Pomerance, C. R. Acad. Sci. Paris (Ser. I) 310 (1990), 343-348.

  74. On the normal behavior of the iterates of some arithmetic functions, P. Erdős, A. Granville, C. Pomerance and C. Spiro, Analytic Number Theory, Proc. Conf. in honor of Paul T. Bateman, B. C. Berndt, et al. eds., Birkhauser, Boston, 1990, pp. 165-204.

  75. Unusually large gaps between consecutive primes, H. Maier and C. Pomerance, Trans. Amer. Math. Soc. 322 (1990), 201-237.

  76. On the least prime in certain arithmetic progressions, A. Granville and C. Pomerance, J. London Math. Soc. (2) 41 (1990), 193-200.

  77. Factoring, C. Pomerance, Cryptology and Computational Number Theory, C. Pomerance, ed., Proc. Symp. Appl. Math. 42, Amer. Math. Soc. Providence, 1990.

  78. Cryptology and computational number theory - an introduction, C. Pomerance, Cryptology and Computational Number Theory, C. Pomerance, ed., Proc. Symp. Appl. Math. 42, Amer. Math. Soc., Providence, 1990.

  79. On a theorem of Besicovitch: values of arithmetic functions that divide their arguments, P. Erdős and C. Pomerance, Indian J. Math. 32 (1990), 279-287.

  80. On the prime divisors of Mersenne numbers, P. Erdős, P. Kiss and C. Pomerance, Acta Arith. 57 (1991), 267-281.

  81. Carmichael's lambda function, P. Erdős, C. Pomerance and E. Schmutz, Acta Arith. 58 (1991), 363-385.

  82. The distribution of Lucas and elliptic pseudoprimes, D.M. Gordon and C. Pomerance, Math. Comp. 57 (1991), 825-838.

  83. Grandes déviations pour certaines fonctions arithmétiques, M. Balazard, J.L. Nicolas, C. Pomerance and G. Tenenbaum, J. Number Theory 40 (1992), 146-164.

  84. The distribution of smooth numbers in arithmetic progressions, A. Balog and C. Pomerance, Proc. Amer. Math. Soc. 115 (1992), 33-43.

  85. A rigorous time bound for factoring integers, H. W. Lenstra, Jr. and C. Pomerance, J. Amer. Math. Soc. 5 (1992), 483-516.

  86. Reduction of huge, sparse matrices over a finite field via created catastrophes, C. Pomerance and J. W. Smith, Experimental Math. 1 (1992), 90-94.

  87. The Riemann zeta function and the one dimensional Weyl-Berry conjecture for fractal drums, M.L. Lapidus and C. Pomerance, Proc. London Math. Soc. (3) 66 (1993), 41-69.

  88. Average case error estimates for the strong probable prime test, I. Damgard, P. Landrock and C. Pomerance, Math. Comp. 61 (1993), 177-194.

  89. Carmichael numbers, C. Pomerance, Nieuw Arch. Wisk. 11 (1993), 199-209.

  90. On elements of sumsets with many prime factors, P. Erdős, C. Pomerance, A. Sárközy and C. L. Stewart, J. Number Theory 44 (1993), 93-104.

  91. An upper bound in Goldbach's conjecture, J.M. Deshouillers, A. Granville, W. Narkiewicz and C. Pomerance, Math. Comp. 61 (1993), 209-213.

  92. Factoring integers with the number field sieve, J. Buhler, H. W. Lenstra, Jr. and C. Pomerance, The development of the number field sieve, A. K. Lenstra and H. W. Lenstra, Jr., eds., Lecture Notes in Math. 1554, pp. 50-94, Springer-Verlag, Berlin, 1993.

  93. A hyperelliptic smoothness test. I, H. W. Lenstra, Jr., J. Pila and C. Pomerance, Phil. Trans. R. Soc. London A 345 (1993), 397-408.

  94. Sixes and sevens, C. Pomerance, Missouri J. Math. Sci. 6 (1994), 62-63.

  95. There are infinitely many Carmichael numbers, W. R. Alford, A. Granville and C. Pomerance, Annals Math. 140 (1994), 703-722.

  96. On the difficulty of finding reliable witnesses, W. R. Alford, A. Granville and C. Pomerance, Algorithmic Number Theory Proceedings (ANTS-I), L. M. Adleman and M.-D. Huang, eds., Lecture Notes in Computer Sci. 877 (1994), Springer-Verlag, Berlin, pp. 1-16.

  97. Dickson polynomials with few fixed points in a finite field, C. Pomerance, J. Sichuan U. (Natural Science Ed.) 31 (1994), 460-464.

  98. On a conjecture of R. L. Graham, F. Y. Cheng and C. Pomerance, Rocky Mtn. J. Math. 24 (1994), 961-975.

  99. The number field sieve, C. Pomerance, Mathematics of Computation, 1943-1993, Fifty Years of Computational Mathematics, W. Gautschi, ed., Proc. Symp. Appl. Math. 48, American Mathematical Society, Providence, 1994, pp. 465-480.

  100. Counting the integers factorable via cyclotomic methods, C. Pomerance and J. Sorenson, J. Algorithms, 19 (1995), 250-265.

  101. On a conjecture of Crandall concerning the qx+1 problem, Z. Franco and C. Pomerance, Math. Comp. 64 (1995), 1333-1336.

  102. Implementing the self initializing quadratic sieve on a distributed network, W.R. Alford and C. Pomerance, Number Theoretic and Algebraic Methods in Computer Science, Proc. of Int'l Moscow Conference, June-July, 1993, A. J. van der Poorten, I. Shparlinski, H. G. Zimmer, eds., World Scientific, 1995, pp. 163-174.

  103. Combinatorial number theory, C. Pomerance and A. Sárközy, Handbook of Combinatorics, R. L. Graham, M. Grötschel, L. Lovász, eds., Elsevier Science B.V., 1995, pp. 967-1018.

  104. On the role of smooth numbers in number theoretic algorithms, C. Pomerance, Proceedings of the Intenational Congress of Mathematicians, Zurich, Switzerland 1994, Birkhauser Verlag, Basel, 1995, pp. 411-422.

  105. Counterexamples to the modified Weyl-Berry conjecture, M.L. Lapidus and C. Pomerance, Math. Trans. Cambridge Phil. Soc. 119 (1996), 167-178.

  106. Symmetric and asymmetric primes, P. Fletcher, W. Lindgren and C. Pomerance, J. Number Theory 58 (1996), 89-99.

  107. Multiplicative independence for random integers, C. Pomerance, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 2, B. Berndt, H. Diamond, A. Hildebrand, eds., Birkhauser, Boston, 1996, pp. 703-711.

  108. On the divisors of n!, P. Erdős, S.W. Graham, A. Ivic and C. Pomerance, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 1, B. Berndt, H. Diamond, A. Hildebrand, eds., Birkhauser, Boston, 1996, pp. 337-355.

  109. A tale of two sieves, C. Pomerance, The Notices of the Amer. Math. Soc. 43 (1996), 1473-1485.

  110. On primes recognizable in deterministic polynomial time, S. Konyagin and C. Pomerance, The mathematics of Paul Erdős, R. L. Graham and J. Nesetril, eds., Springer-Verlag, Berlin, 1997, pp. 176-198.

  111. A search for Wieferich and Wilson primes, R. Crandall, K. Dilcher and C. Pomerance, Math. Comp. 66 (1997), 433-449.

  112. On locally repeated values of certain arithmetic functions, IV, P. Erdős, C. Pomerance and A. Sárközy, The Ramanujan J. 1 (1997), 227-241.

  113. Automaticity II: Descriptional complexity in the unary case, C. Pomerance, J.M. Robson and J. Shallitt, Theoretical Computer Sci. 180 (1997), 181-201.

  114. Paul Erdős, number theorist extraordinaire, C. Pomerance, The Notices of the Amer. Math. Soc. 45 (1998), 19-23.

  115. Rigorous discrete logarithm computations in finite fields via smooth polynomials, R. Lovorn Bender and C. Pomerance, AMS/IP Studies in Advanced Mathematics 7 (1998), 221-232.

  116. Euler's function in residue classes, T. Dence and C. Pomerance, The Ramanujan Journal 2 (1998), 7-20.

  117. On the distribution of champs, A. Ivic and C. Pomerance, Proceedings of the Fifth Conference of the Canadian Number Theory Association, R. Gupta and K.S. Williams, eds., CRM Proc. 19 (1999), 133-139.

  118. Residue classes free of values of Euler's function, K. Ford, S. Konyagin and C. Pomerance, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 805-812.

  119. On the solutions to φ(n) = φ(n+k), S.W. Graham, J.J. Holt and C. Pomerance, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 867-882.

  120. Primes and factorization, J. Grantham and C. Pomerance, Handbook of Discrete Mathematics, K.H. Rosen, ed., CRC Press, 1999.

  121. Small values of the Carmichael function and cryptographic applications, J. Friedlander, C. Pomerance and I. E. Shparlinski, Proc. Workshop on Cryptography and Computational Number Theory (CCNT'99), K.-Y. Lam, I. E. Shparlinski, H. Wang, and C. Xing, eds., Birkhäuser, 2001, pp. 25-32.

  122. The expected number of random elements to generate a finite abelian group, C. Pomerance, Periodica Mathematica Hungarica 43 (2001), 191-198.

  123. Period of the power generator and small values of the Carmichael function, J. Friedlander, C. Pomerance and I. E. Shparlinski, Math. Comp., 70 (2001), 1591-1605. Corrigendum, op. cit., 71 (2002), 1803-1806.

  124. Two contradictory conjectures concerning Carmichael numbers, A. Granville and C. Pomerance, Math. Comp., 71 (2001), 883-908.

  125. On the problem of uniqueness for the maximal Stirling number(s) of the second kind, E.R. Canfield and C. Pomerance, Integers, 2 (2002), paper A1, 13 pp.

  126. On some problems of Makowski-Schinzel and Erdős concerning the arithmetical functions φ and σ, F. Luca and C. Pomerance, Colloq. Math., 92 (2002), 111-130.

  127. Smooth orders and cryptographic applications, C. Pomerance and I.E. Shparlinski, Proc. ANTS-V, Sydney, Australia, Springer Lecture Notes in Computer Science 2369, (2002), pp. 338-348.

  128. A hyperelliptic smoothness test. II, H. W. Lenstra, Jr., J. Pila and C. Pomerance, Proc. London Math. Soc., (3) 84 (2002), 105-146.

  129. Ruth-Aaron numbers revisited, C. Pomerance, Paul Erdős and his Mathematics, (Budapest, 1999), Bolyai Soc. Math. Stud. 11, János Bolyai Math. Soc., Budapest, 2002, pp. 567-579.

  130. Primitive roots: a survey, S. Li and C. Pomerance, in New Aspects of Analytic Number Theory (RIMS Kokyuroku No. 1274) (Y. Tanigawa, ed.), and also in Number Theoretic Methods---Future Trends, C. Jia and S. Kanemitsu, eds., Dev. Math. 8, pp. 219-231, Kluwer Academic Publishers, Dordrecht 2002.

  131. On generalizing Artin's conjecture on primitive roots to composite moduli, S. Li and C. Pomerance, J. Reine Angew. Math. 556 (2003), 205-224.

  132. Timed fair exchange of arbitrary signatures, J. A. Garay and C. Pomerance, in Financial Cryptography, 7th International Conference, FC 2003, Lecture Notes in Computer Science 2742, Springer, New York, 2003, pp. 190-207.

  133. Multiplicative structure of values of the Euler function, W. D. Banks, J. B. Friedlander, C. Pomerance and I. E. Shparlinski, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 29-47.

  134. Heuristics for class numbers of prime-power real cyclotomic fields, J. Buhler, C. Pomerance and L. Robertson, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 149-157.

  135. Prime numbers and the search for extraterrestrial intelligence, C. Pomerance, in Mathematical Adventures for Students and Amateurs, D. Hayes and T. Shubin, eds., M.A.A., 2004, pp. 1-4.

  136. The largest prime factor of a Mersenne number, L. Murata and C. Pomerance, in Number Theory, CNTA Proceedings, Montreal, 2002, CRM Proc. Lecture Notes, 36, Amer. Math. Soc., Providence, RI, 2004, pp. 209-218.

  137. On the binary expansions of algebraic numbers, D. H. Bailey, J. M. Borwein, R. E. Crandall, and C. Pomerance, J. Théorie des Nombres Bordeaux 16 (2004), 487-518.

  138. On the distribution in residue classes of integers with a fixed sum of digits, C. Mauduit, C. Pomerance and A. Sárközy), Ramanujan J., special issue in honor of J.-L. Nicolas 9 (2005), 45-62.

  139. Products of ratios of consecutive integers, R. de la Bretèche, C. Pomerance, and G. Tenenbaum, Ramanujan J., special issue in honor of J.-L. Nicolas 9 (2005), 131-138.

  140. The iterated Carmichael λ-function and the number of cycles of the power generator, G. Martin and C. Pomerance, Acta Arith. 118 (2005), 305-335.

  141. On the period of the linear congruential and power generators, P. Kurlberg and C. Pomerance, Acta Arith. 119 (2005), 149-169.
    Extended abstract, to appear in the proceedings of the Turku conference on algorithmic number theory.

  142. Finding the group structure of elliptic curves over finite fields, J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, Bull. Austral. Math. Soc. 72 (2005), 251-263.

  143. Primality testing with Gaussian periods, H. W. Lenstra, Jr. and C. Pomerance, preprint.

  144. On the average number of divisors of the Euler function, F. Luca and C. Pomerance, Publ. Math. Debrecen, 70 (2007), 125-148.

  145. Sieving by large integers and covering systems of congruences, M. Filaseta, K. Ford, S. Konyagin, C. Pomerance, and G. Yu, J. Amer. Math. Soc., 20 (2007), 495-517.

  146. Maximal height of divisors of xn-1, C. Pomerance and N. C. Ryan, Illinois J. Math., 51 (2007), 597-604.

  147. Irreducible radical extensions and Euler-function chains, F. Luca and C. Pomerance, pp. 351-362 in Combinatorial Number Theory, Landman et al., eds., de Gruyter, 2007, and in Integers, 7(2) (2007), paper A25.

  148. Smooth numbers and the quadratic sieve, C. Pomerance, in Surveys in algorithmic number theory, J. P. Buhler and P. Stevenhagen, eds., Math. Sci. Res. Inst. Pub. 44, Cambridge U. Press, New York, 2008, pp. 69-81.

  149. Elementary thoughts on discrete logarithms, C. Pomerance, in Surveys in algorithmic number theory, J. P. Buhler and P. Stevenhagen, eds., Math. Sci. Res. Inst. Pub. 44, Cambridge U. Press, New York, 2008, pp. 385-396.

  150. Computational number theory, C. Pomerance, Princeton Companion to Mathematics, W. T. Gowers, ed., to appear.

  151. On the proportion of numbers coprime to a given integer, P. Erdős, F. Luca, and C. Pomerance, Proceedings of the Anatomy of Integers Conference, Montreal, March 2006, J.-M. De Koninck, A. Granville, F. Luca, eds., CRM Proceedings and Lecture Notes, vol. 46 (2008), 47-64.

  152. Rank statistics for a family of elliptic curves over a function field, C. Pomerance and I. E. Shparlinski, Pure and Appl. Math. Q., to appear.

  153. On the distribution of pseudopowers, S. V. Konyagin, C. Pomerance, and I. E. Shparlinski, Canad. J. Math., to appear.

  154. On pseudosquares and pseudopowers, C. Pomerance and I. E. Shparlinski, Proceedings of Integers 07 Conference, to appear.

  155. Sets with prescribed arithmetic densities, F. Luca, C. Pomerance, and S. Porubsky, submitted for publication.

  156. On the range of the iterated Euler function, F. Luca and C. Pomerance, Proceedings of Integers 07 Conference, to appear.

  157. On Giuga numbers, F. Luca, C. Pomerance, and I. E. Shparlinski, Int. J. Mod. Math., to appear.

  158. Primality testing: variations on a theme of Lucas, C. Pomerance, to appear in the Proceedings of the 13th Meeting of the Fibonacci Association.

  159. On the distribution of sociable numbers , M. Kobayashi, P. Pollack, and C. Pomerance, submitted for publication.

  160. Error estimates for the Davenport--Heilbronn theorems, K. Belabas, M. Bhargava, and C. Pomerance, submitted for publication.

    Last modified on September 4, 2008 by the owner.