A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman sums. (English) Zbl 0966.11018

The author describes a numerical test in order to determine whether a given sequence of numbers can occur as Fourier coefficients of a Maass wave form, without knowing its eigenvalue. The test can be extended to holomorphic newforms as well. In particular a negative answer is obtained for the Kloosterman sums \(\pm S(1,1;p)/ \sqrt p\) for primes \(p\).
Reviewer: A.Krieg (Aachen)


11F30 Fourier coefficients of automorphic forms
11L05 Gauss and Kloosterman sums; generalizations
11Y99 Computational number theory
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