Variance of GL(2) Fourier coefficients in arithmetic progressions
Number Theory
2026-05-22 v2
Abstract
We improve a result of Lau and Zhao on the variance of Fourier coefficients of primitive cuspidal modular forms for SL2(Z) in arithmetic progressions. This is achieved by using bounds on the first moment of Rankin-Selberg L-functions in the height aspect and non-trivial estimates for shifted convolution sums.
Keywords
Cite
@article{arxiv.2603.15197,
title = {Variance of GL(2) Fourier coefficients in arithmetic progressions},
author = {Laurent Montaigu},
journal= {arXiv preprint arXiv:2603.15197},
year = {2026}
}