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arXiv · 1610.05380

Cancellation in the Additive Twists of Fourier Coefficients for $\mathrm{GL}_2$ and $\mathrm{GL}_3$ over Number Fields

Zhi Qi
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Abstract

In this article, we study the sum of additively twisted Fourier coefficients of an irreducible cuspidal automorphic representation of $\mathrm{GL}_2$ or $\mathrm{GL}_3$ over an arbitrary number field. When the representation is unramified at all non-archimedean places, we prove the Wilton type bound for $\mathrm{GL}_2$ and the Miller type bound for $\mathrm{GL}_3$ which are uniform in terms of the additive character.

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Zhi Qi. 2016-10-17. Cancellation in the Additive Twists of Fourier Coefficients for $\mathrm{GL}_2$ and $\mathrm{GL}_3$ over Number Fields. https://arxiv.org/abs/1610.05380

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