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October 2000 A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman sums
Andrew R. Booker
Experiment. Math. 9(4): 571-581 (October 2000).

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 $\pm S(1,1;p)\big/\hskip-1pt\sqrt p$are not the coefficients of a Maass form with small level and eigenvalue. Source code and the calculated Kloosterman sums are available electronically.

Citation

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Andrew R. Booker. "A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman sums." Experiment. Math. 9 (4) 571 - 581, October 2000.

Information

Published: October 2000
First available in Project Euclid: 20 February 2003

zbMATH: 0966.11018
MathSciNet: MR1806292

Subjects:
Primary: 11F30
Secondary: 11L05, 11Y35

Rights: Copyright © 2000 A K Peters, Ltd.

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Vol.9 • No. 4 • October 2000
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