Double weighted sum involving $\mathrm{GL}(2)$ Fourier coefficients

Himanshi Chanana; Mohd Harun

Double weighted sum involving $\mathrm{GL}(2)$ Fourier coefficients

Number Theory 2026-06-29 v1

Authors: Himanshi Chanana , Mohd Harun

Abstract

This article proves non-trivial estimates for a bilinear sum involving the Fourier coefficients of a Hecke-holomorphic or Hecke-Maass cusp form for $\mathrm{SL}(2,\mathbb{Z})$ . As corollaries, we draw interesting results related to non-trivial bounds of different shifted convolution sums and summatory functions.

Cite

@article{arxiv.2606.29822,
  title  = {Double weighted sum involving $\mathrm{GL}(2)$ Fourier coefficients},
  author = {Himanshi Chanana and Mohd Harun},
  journal= {arXiv preprint arXiv:2606.29822},
  year   = {2026}
}

Comments

16 pages, To appear in IJNT