Abstract
We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums +/-S(1, 1;p)/rootP are not the coefficients of a Maass form with small level and eigenvalue. Source code and the calculated Kloosterman sums are available electronically.
| Translated title of the contribution | A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman |
|---|---|
| Original language | English |
| Pages (from-to) | 571 - 581 |
| Number of pages | 11 |
| Journal | Experimental Mathematics |
| Volume | 9 (4) |
| Publication status | Published - 2000 |
Bibliographical note
Publisher: A K Peters LtdOther identifier: IDS number 393JJ