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|
|Pages (from-to)||571 - 581|
|Number of pages||11|
|Publication status||Published - 2000|
Bibliographical notePublisher: A K Peters Ltd
Other identifier: IDS number 393JJ