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On modular signs. (English) Zbl 1272.11061

Summary: We consider some questions related to the signs of Hecke eigenvalues or Fourier coefficients of classical modular forms. One problem is to determine to what extent those signs, for suitable sets of primes, determine uniquely the modular form, and we give both individual and statistical results. The second problem, which has been considered by a number of authors, is to determine the size, in terms of the conductor and weight, of the first sign-change of Hecke eigenvalues. Here we improve the recent estimate of H. Iwaniec, W. Kohnen and J. Sengupta [Int. J. Number Theory 3, No. 3, 355–363 (2007; Zbl 1219.11066)].

MSC:

11F30 Fourier coefficients of automorphic forms
11F25 Hecke-Petersson operators, differential operators (one variable)

Citations:

Zbl 1219.11066
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References:

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