On modular signs
Number Theory
2015-05-14 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0911.2269,
title = {On modular signs},
author = {Emmanuel Kowalski and Yuk Kam Lau and Kannan Soundararajan and Jie Wu},
journal= {arXiv preprint arXiv:0911.2269},
year = {2015}
}
Comments
23 pages, 1 figure; new version with new coauthor and strong improvements of two of the two main results.