On modular signs

Details On modular signs On modular signs

2009-11-11

arxiv.org/abs/0911.2269v2

Mathematics

Number Theory

23 pages, 1 figure; new version with new coauthor and strong improvements of two of the two main results.

Scientific paper

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 significantly the recent estimate of Iwaniec, Kohnen and Sengupta.

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