Resonances and \(\Omega\)-results for exponential sums related to Maass forms for \(\mathrm{SL}(n, \mathbb{Z})\)

DOI10.1016/j.jnt.2015.01.014zbMath1357.11067arXiv1405.7190OpenAlexW1976510452MaRDI QIDQ2344344

Anne-Maria Ernvall-Hytönen, Jesse Jääsaari, Esa V. Vesalainen

Publication date: 13 May 2015

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.7190

zbMATH Keywords

resonanceVoronoi summation formulaFourier coefficients of autormorphic forms on \(\mathrm{GL}(n)\)short exponential sum

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Fourier coefficients of automorphic forms (11F30) Trigonometric and exponential sums (general theory) (11L03)

Related Items (9)

Bounds for average toward the resonance barrier for \(\mathrm{GL}(3) \times\mathrm{GL}(2)\) automorphic forms ⋮ Spectral square moments of a resonance sum for Maass forms ⋮ Double square moments and bounds for resonance sums of cusp forms ⋮ On short sums involving Fourier coefficients of Maass forms ⋮ On sums involving Fourier coefficients of Maass forms for \(\mathrm{SL}(3,\mathbb Z)\) ⋮ Computing the Laplace eigenvalue and level of Maass cusp forms ⋮ Resonance sums for Rankin-Selberg products of \(\mathrm{SL}_m(\mathbb{Z})\) Maass cusp forms ⋮ Exponential sums related to Maass forms ⋮ Bounds toward hypothesis S for cusp forms

Uses Software

• GL(n)pack

Cites Work

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