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 eigencusp forms for the full modular group SL 2(ℤ). We also prove a similar kind of quantitative result for the number of sign changes of the q-exponents $c(p)~(p \mbox{~vary ~over ~primes})$ of certain generalized modular functions for the congruence subgroup Γ0(N), where N is square-free.