  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
$SL_2(\mathbb{Z})$. 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.
