A short note on sign changes

Abstract

In this paper, we present a quantitative result for the number of sign changes for the sequences $\{a(n^j){\}}_{n\ge 1},j=2,3,4$ of the Fourier coefficients of normalized Hecke eigen cusp forms for the full modular group $S{L}_2(\mathbb{Z})$. We also prove a similar kind of quantitative result for the number of sign changes of the $q$-exponents $c(p)(pvaryoverprimes)$ of certain generalized modular functions for the congruence subgroup ${\Gamma }_0(N)$, where $N$ is square-free.

6 pages