First moments of Rankin-Selberg convolutions of automorphic forms on \(\mathrm{GL}(2)\)

DOI10.1007/s40993-021-00281-xzbMath1487.11048arXiv2008.12035OpenAlexW3200314743MaRDI QIDQ1983160

Jeffrey Hoffstein, Min Lee, Maria Năstăsescu

Publication date: 15 September 2021

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

Full work available at URL: https://arxiv.org/abs/2008.12035

zbMATH Keywords

Rankin-Selberg \(L\)-seriesshifted convolutionsBruggeman-Kuznetsov trace formulaspectral first moments

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) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (1)

An extension of Venkatesh’s converse theorem to the Selberg class

Uses Software

• DLMF

Cites Work

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• Multiple Dirichlet series and shifted convolutions
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• Determination of modular forms by twists of critical \(L\)-values
• A trace formula for the scalar product of Hecke series and its applications
• A conjectural extension of Hecke's converse theorem
• Explicit calculations with Eisenstein series
• The holomorphic kernel of the Rankin-Selberg convolution
• Additive twists and a conjecture by Mazur, Rubin and Stein
• First moment of Rankin-Selberg central \(L\)-values and subconvexity in the level aspect
• Stable averages of central values of Rankin-Selberg \(L\)-functions: some new variants
• Determining modular forms of general level by central values of convolution L-functions
• Distinguishing Hecke eigenvalues of primitive cusp forms
• Determination of ${\bf GL}(2)$ Maass forms from twists in the level aspect

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