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On sums of Fourier coefficients of cusp forms twisted with additive characters (2311.00006v1)
Published 30 Oct 2023 in math.NT
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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