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arXiv · 2606.29822

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

Himanshi Chanana·Mohd Harun
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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.

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Himanshi Chanana, Mohd Harun. 2026-06-29. Double weighted sum involving $\mathrm{GL}(2)$ Fourier coefficients. https://arxiv.org/abs/2606.29822

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