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 be the nth 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.
