On sums of Fourier coefficients of cusp forms twisted with additive characters

Zihao Liu

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arXiv · 2311.00006

On sums of Fourier coefficients of cusp forms twisted with additive characters

Zihao Liu

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Abstract

When $a_n$ is the $n$'th coefficient of some holomorphic cusp form, we prove a variety of Omega results for the twisted sum $\sum_{n\le x}a_ne^{2\pi in\alpha}$ and discuss their applications to the Ramanujan $\tau$-function and sums of $a_n$ over arithmetic progressions.

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Zihao Liu. 2023-10-30. On sums of Fourier coefficients of cusp forms twisted with additive characters. https://arxiv.org/abs/2311.00006

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