First moment of Hecke eigenvalues at the integers represented by binary quadratic forms
Article Type
Research Article
Publication Title
Indagationes Mathematicae
Abstract
In the article, we consider a question concerning the estimation of summatory function of the Fourier coefficients of Hecke eigenforms indexed by a sparse set of integers. In particular, we provide an estimate for the following sum; S(f,Q;X)≔∑♭[Formula presented]λf(n),where ♭ means that sum runs over the square-free positive integers, λf(n) denotes the normalised nth Fourier coefficients of a Hecke eigenform f of integral weight k for the congruence subgroup Γ0(N) and Q is a primitive integral positive-definite binary quadratic forms of fixed discriminant D<0 with the class number h(D)=1. As a consequence, we determine the size, in terms of conductor of associated L-function, for the first sign change of Hecke eigenvalues indexed by the integers which are represented by Q. This work is an improvement and generalisation of the previous results.
First Page
713
Last Page
728
DOI
10.1016/j.indag.2024.08.001
Publication Date
5-1-2025
Recommended Citation
Pandey, Manish Kumar and Vaishya, Lalit, "First moment of Hecke eigenvalues at the integers represented by binary quadratic forms" (2025). Journal Articles. 5371.
https://digitalcommons.isical.ac.in/journal-articles/5371