Convolution formula for the sums of generalized Dirichlet \(L\)-functions

DOI10.4171/rmi/1106zbMath1472.11149arXiv1709.01365OpenAlexW2957892156MaRDI QIDQ2280516

Olga G. Balkanova, Dmitriy A. Frolenkov

Publication date: 18 December 2019

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.01365

zbMATH Keywords

symmetric square \(L\)-functionsKuznetsov trace formulaprime geodesic theoremgeneralized Kloosterman sumsgeneralized Dirichlet \(L\)-functions

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (5)

Prime geodesics and averages of the Zagier L-series ⋮ Spectral decomposition formula and moments of symmetric square $L$-functions ⋮ Bounds for a spectral exponential sum ⋮ Prime geodesic theorem for the Picard manifold ⋮ Non-vanishing of Maass form symmetric square \(L\)-functions

Uses Software

• DLMF

Cites Work

• Central value of the symmetric square \(L\)-functions related to Hecke-Maass forms
• Double Dirichlet series and quantum unique ergodicity of weight one-half Eisenstein series
• Eisenstein series of \(1\over 2\)-integral weight and the mean value of real Dirichlet L-series
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• The cubic moment of central values of automorphic \(L\)-functions
• The mean value of symmetric square \(L\)-functions
• On the Kuznetsov formula
• Beyond endoscopy via the trace formula: 1. Poisson summation and isolation of special representations
• The binary additive divisor problem
• The prime geodesic theorem
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