New error term for the fourth moment of automorphic \(L\)-functions

DOI10.1016/J.JNT.2016.09.023zbMath1420.11087arXiv1602.08203OpenAlexW2964147034MaRDI QIDQ730047

Olga G. Balkanova, Dmitriy A. Frolenkov

Publication date: 23 December 2016

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

Full work available at URL: https://arxiv.org/abs/1602.08203

zbMATH Keywords

fourth momentsubconvexityprimitive formssimultaneous non-vanishing

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Automorphic forms, one variable (11F12)

Related Items (2)

The fifth moment of modular \(L\)-functions ⋮ The first moment of twisted Hecke \(L\)-functions with unbounded shifts

Cites Work

• Kloosterman sums and Fourier coefficients of cusp forms
• Bounds for automorphic \(L\)-functions. II
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• Mollification of the fourth moment of automorphic \(L\)-functions and arithmetic applications.
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• On Selberg's eigenvalue conjecture
• The shifted fourth moment of automorphic $L$-functions of prime power level
• The distribution of αp modulo one
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
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