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arXiv · 2111.09524

Bounds for short character sums for $GL(2) \times GL(3)$ twists

Aritra Ghosh
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Abstract

Let $π$ be a $SL(3,\mathbb{Z})$ Hecke Maass-cusp form, $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or Maass-cusp form with normalized Fourier coefficients $λ_π(r,n) \text{ and }λ_{f}(n)$ respectively and $χ$ be any non-trivial character mod $p$ where $p$ is a prime. Then we have $$S_{π,f,χ}(N)\ll_{π, f, ε} N^{3/4}p^{11/16 +{η/4}}(Np)^ε.$$

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Aritra Ghosh. 2024-12-03. Bounds for short character sums for $GL(2) \times GL(3)$ twists. https://arxiv.org/abs/2111.09524

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