Spectral mean values of Maass waveform \(L\)-functions

DOI10.1016/0022-314X(92)90092-4zbMath0759.11026MaRDI QIDQ1201730

Yoichi Motohashi

Publication date: 17 January 1993

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

zbMATH Keywords

Riemann zeta-functionasymptotic formulaerror termHecke seriesfourth power meanKuznetsov trace formulaMaass waveform \(L\)-functionsspectral mean values

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Quantitative non-vanishing of central values of certain \(L\)-functions on \(\mathrm{GL}(2) \times \mathrm{GL}(3)\) ⋮ Nonvanishing of central \(L\)-values of Maass forms ⋮ Moments of central 𝐿-values for Maass forms over imaginary quadratic fields ⋮ On the binary additive divisor problem ⋮ Some \(\Omega\)-results related to the fourth power moment of the Riemann zeta-function and the additive divisor problem ⋮ The binary additive divisor problem ⋮ An explicit formula for the second moment of Maass form symmetric square \(L\)-functions ⋮ Prime geodesic theorem for the Picard manifold ⋮ Complete asymptotic expansions associated with Epstein zeta-functions ⋮ The Selberg trace formula as a Dirichlet series ⋮ On exponential sums with Hecke series at central points ⋮ Unnamed Item ⋮ Spectral means of central values of automorphic 𝐿-functions for 𝐺𝐿(2) ⋮ An explicit formula for the fourth power mean of the Riemann zeta- function ⋮ Asymptotic behaviors of means of central values of automorphic \(L\)-functions for \(\mathrm{GL}(2)\) ⋮ On sums of Hecke series in short intervals

Cites Work

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