Sign changes of coefficients of half integral weight modular forms

Details Sign changes of coefficients of half integral weight modular forms Sign changes of coefficients of half integral weight modular forms

2007-09-13

arxiv.org/abs/0709.2001v1

Mathematics

Number Theory

Scientific paper

For a half integral weight modular form $f$ we study the signs of the Fourier coefficients $a(n)$. If $f$ is a Hecke eigenform of level $ N$ with real Nebentypus character, and $t$ is a fixed square-free positive integer with $a(t)\neq 0$, we show that for all but finitely many primes $p$ the sequence $(a(tp^{2m}))_{m}$ has infinitely many signs changes. Moreover, we prove similar (partly conditional) results for arbitrary cusp forms $f$ which are not necessarily Hecke eigenforms.

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