The distribution of Fourier coefficients of cusp forms over sparse sequences
Volume 163 / 2014
Acta Arithmetica 163 (2014), 101-110
MSC: Primary 11F30; Secondary 11F66.
DOI: 10.4064/aa163-2-1
Abstract
Let $\lambda_f(n)$ be the $n$th normalized Fourier coefficient of a holomorphic Hecke eigenform $f(z)\in S_{k}(\Gamma)$. We establish that $\sum_{n \leq x}\lambda_f^2(n^j)=c_{j} x+O(x^{1-\frac{2}{(j+1)^2+1}})$ for $j=2,3,4,$ which improves the previous results. For $j=2$, we even establish a better result.
