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arXiv · 1405.7190

Resonances and $Ω$-results for Exponential Sums Related to Maass Forms for $\mathrm{SL}(n,\mathbb Z)$

Anne-Maria Ernvall-Hytönen·Jesse Jääsaari·Esa V. Vesalainen
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Abstract

We obtain resonances for short exponential sums involving Fourier coefficients of Maass forms for $\mathrm{SL}(n,\mathbb Z)$. This involves deriving asymptotics for the integrals appearing in the $\mathrm{GL}(n)$ Voronoi summation formula. As an application, we also prove an $Ω$-result for short sums of Fourier coefficients.

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Anne-Maria Ernvall-Hytönen, Jesse Jääsaari, Esa V. Vesalainen. 2014-08-06. Resonances and $Ω$-results for Exponential Sums Related to Maass Forms for $\mathrm{SL}(n,\mathbb Z)$. https://arxiv.org/abs/1405.7190

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