Angular changes of Fourier coefficients at primes

Abstract

We study the angle changes of Fourier coefficients of cusp forms and q-exponents of generalized modular functions at primes. More precisely, we prove that both these subsequences, under certain conditions, fall infinitely often outside any given wedge \(\mathcal {W}(\theta _1, \theta _2):=\{re^{i\theta }: r>0, \theta \in [\theta _1,\theta _2]\}\) with \(0\le \theta _2-\theta _1< \pi \).