On some exponential sums involving Maass forms over arithmetic progressions

DOI10.1016/J.JNT.2015.08.010zbMath1330.11052OpenAlexW1841005954MaRDI QIDQ897529

Xiaofei Yan

Publication date: 7 December 2015

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.08.010

zbMATH Keywords

exponential sumsarithmetic progressionFourier coefficients of Maass forms

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Gauss and Kloosterman sums; generalizations (11L05) Fourier coefficients of automorphic forms (11F30)

Related Items (2)

Exponential sums involving automorphic forms for \(\mathrm{GL}(3)\) over arithmetic progressions ⋮ Sums of Fourier coefficients of cusp forms of level 𝐷 twisted by exponential functions over arithmetic progressions

Cites Work

• Resonance between automorphic forms and exponential functions
• The highly oscillatory behavior of automorphic distributions for \(\text{SL}(2)\)
• Some remarks on odd Maass wave forms (and a correction to [1)]
• Rankin-Selberg \(L\)-functions in the level aspect.
• Exponential sums involving Maass forms
• SUMS OF FOURIER COEFFICIENTS OF CUSP FORMS
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
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