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# Some sample theorems

The proof which is below is correct, but unmotivated. Perhaps we can find an alternate proof which provides more insight

Proof. If for all but a finite number of square-free positive integers , then by lemma:squareclasses the Fourier coefficients of are supported on only a finite number of square classes. By Theorem 3 of [3] the weight of must be of and at weight must be in the span of the theta series , contrary to assumption.

By thm:nonzerolifts, we see that it we can always find nonzero Shimura lifts.

Here we have some displayed and aligned equations.

Here is an unnumbered displayed equation:

Here is a numbered displayed equation:

 (1)

Here is the same expression, but inline and not displayed. Notice it is set smaller and the summation indeices are placed differently: Note I need to use \$ to surround my formula when in an inline mode.

For an aligned display we have

A numbered version is given by

 (2) (3)

A version with only one number associated to the group of equations is given by

 (4)

Something with cases

This should be more than enough displayed equations for the average person. Gosh, I sure hope this paper gets accepted. More remarks of little permanent consequence.

Let's get the other references in now. See [1] and [2].

Next: Bibliography Up: Sample LATEX document Previous: Preliminaries
Thomas R. Shemanske 2000-07-07