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A short note on sign changes (1301.0883v2)
Published 5 Jan 2013 in math.NT
Abstract: In this paper, we present a quantitative result for the number of sign changes for the sequences ${a(nj)}_{n\ge 1}, j=2,3,4$ of the Fourier coefficients of normalized Hecke eigen cusp forms for the full modular group $SL_2(\mathbb{Z})$. We also prove a similar kind of quantitative result for the number of sign changes of the $q$-exponents $c(p) (p {vary over primes})$ of certain generalized modular functions for the congruence subgroup $\Gamma_0(N)$, where $N$ is square-free.