A note on the mean value of the zeta and L-functions. I

DOI10.3792/pjaa.61.222zbMath0573.10027OpenAlexW2000186254MaRDI QIDQ1063062

Yoichi Motohashi

Publication date: 1985

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.61.222

zbMATH Keywords

asymptotic expansionRiemann zeta-functionanalytic continuationmean valuesPoisson summation formulaDirichlet L-functionsmean square estimates of L-functions

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (16)

Asymptotic expansions of the mean values of Dirichlet \(L\)-functions. III ⋮ On fractional moments of Dirichlet \(L\)-functions ⋮ The mean values of Dirichlet L-functions at integer points and class numbers of cyclotomic fields ⋮ Mean square values of Dirichlet \(L\)-functions associated to fixed order characters ⋮ An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial ⋮ Complete asymptotic expansions associated with various zeta-functions ⋮ Asymptotic expansions of the mean values of Dirichlet \(L\)-functions ⋮ On fractional moments of Dirichlet \(L\)-functions. II ⋮ Dirichlet \(L\)-function and power series for Hurwitz zeta function ⋮ Functional equations for double series of Euler type with coefficients ⋮ Asymptotic expansions of the mean square of Dirichlet L-functions ⋮ An application of the Mellin-Barnes type of integral to the mean square of \(L\)-functions ⋮ On discrete mean values of Dirichlet $L$-functions ⋮ Explicit formulas and asymptotic expansions for certain mean square of Hurwitz zeta-functions ⋮ A note on the mean value of the zeta and L-functions. II ⋮ Discrete mean values of Hurwitz zeta-functions

Cites Work

• An asymptotic series for the mean value of Dirichlet \(L\)-functions
• The mean-value of the Riemann zeta function

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