English

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

Number Theory 2014-08-07 v2

Abstract

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

Keywords

Cite

@article{arxiv.1405.7190,
  title  = {Resonances and $\Omega$-results for Exponential Sums Related to Maass Forms for $\mathrm{SL}(n,\mathbb Z)$},
  author = {Anne-Maria Ernvall-Hytönen and Jesse Jääsaari and Esa V. Vesalainen},
  journal= {arXiv preprint arXiv:1405.7190},
  year   = {2014}
}