Spectral decomposition formula and moments of symmetric square $L$-functions

DOI10.4213/im9330earXiv2011.05952OpenAlexW4387732149MaRDI QIDQ6085102

Olga G. Balkanova

Publication date: 2 December 2023

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.05952

zbMATH Keywords

Gauss sumsEisenstein series\(L\)-functionsKuznetsov trace formula

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) 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) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Cites Work

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• Kloosterman sums and Fourier coefficients of cusp forms
• The mean value of symmetric square \(L\)-functions
• Density theorems and the mean value of arithmetical functions in short intervals
• The first moment of Maaß form symmetric square \(L\)-functions
• On Kuznetsov-Bykovskii's formula of counting prime geodesics
• Convolution formula for the sums of generalized Dirichlet \(L\)-functions
• Kloosterman sums and Fourier coefficients of Eisenstein series
• The fifth moment of modular \(L\)-functions
• On the Holomorphy of Certain Dirichlet Series
• The prime geodesic theorem
• Bykovskii-Type Theorem for the Picard Manifold
• Prime geodesics and averages of the Zagier L-series
• Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method
• Modular Forms

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