A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)

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 contributionA test for identifying Fourier coefficients of automorphic forms and application to Kloosterman
Original languageEnglish
Pages (from-to)571 - 581
Number of pages11
JournalExperimental Mathematics
Volume9 (4)
Publication statusPublished - 2000

Bibliographical note

Publisher: A K Peters Ltd
Other identifier: IDS number 393JJ

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