The zeta-function of the additive divisor problem and spectral decomposition of the automorphic Laplacian

DOI10.1007/BF01104973zbMath0609.10023MaRDI QIDQ1086605

L. A. Takhtadzhyan, A. I. Vinogradov

Publication date: 1987

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

eigenfunctionsasymptotic formulameromorphic continuationzeta-functionadditive divisor problemautomorphic Laplaciansum of Kloosterman sumsorder estimateproduct of two Eisenstein-Maass series

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (2)

Analytic continuation of \(\zeta _ 3(s,k)\) to the critical strip. Arithmetic part ⋮ On the Topography of Maass Waveforms for PSL(2, Z)

Cites Work

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• Estimates of the eigenvalues of Hecke operators in the space of cusp forms of weight 0
• Kloosterman sums and Fourier coefficients of cusp forms
• Sums of Kloosterman sums
• An Additive Divisor Problem

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