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arXiv · 1804.09702

On Short Sums Involving Fourier Coefficients of Maass Forms

Jesse Jääsaari
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Abstract

We study sums of Hecke eigenvalues of Hecke-Maass cusp forms for the group $\mathrm{SL}(n,\mathbb Z)$, with general $n\geq 3$, over certain short intervals under the assumption of the generalised Lindel\"of hypothesis and a slightly stronger upper bound concerning the exponent towards the Ramanujan-Petersson conjecture that is currently known. In particular, in this case we evaluate the second moment of the sums in question asymptotically.

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Jesse Jääsaari. 2018-04-25. On Short Sums Involving Fourier Coefficients of Maass Forms. https://arxiv.org/abs/1804.09702

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