Resonance and rapid decay of exponential sums of Fourier coefficients of a Maass form for \(\mathrm{GL}_m(\mathbb Z)\)

DOI10.1007/s11425-014-4955-3zbMath1386.11069arXiv1411.6022OpenAlexW2155293233MaRDI QIDQ892770

Xiu Min Ren, Yangbo Ye

Publication date: 12 November 2015

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.6022

zbMATH Keywords

Fourier coefficientsresonancecusp form for \(\mathrm{GL}_m(\mathbb Z)\)Voronoi's summation formula

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Fourier coefficients of automorphic forms (11F30)

Related Items (12)

Shifted convolution sums for higher rank groups ⋮ 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 ⋮ Analytic twists of GL2×GL2$\rm GL_2\times \rm GL_2$ automorphic forms ⋮ Double square moments and bounds for resonance sums of cusp forms ⋮ Improved subconvexity bounds for 𝐺𝐿(2)×𝐺𝐿(3) and 𝐺𝐿(3) 𝐿-functions by weighted stationary phase ⋮ The Bombieri–Vinogradov Theorem on Higher Rank Groups and its Applications ⋮ Average behavior of the triple divisor function over values of quadratic form ⋮ On exponential sums for coefficients of general L-functions ⋮ Shifted convolution sums of \(\mathrm{GL}(m)\) cusp forms with \(\Theta\)-series ⋮ Further improvement on bounds for L-functions related to GL(3) ⋮ Bounds toward hypothesis S for cusp forms

Uses Software

• GL(n)pack

Cites Work

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