A note on the mean value of the zeta and \(L\)-functions. XIII.

DOI10.3792/pjaa.78.87zbMath1116.11066OpenAlexW2004053257MaRDI QIDQ1848140

Yoichi Motohashi, Roelof Wichert Bruggeman

Publication date: 31 October 2002

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

Full work available at URL: https://projecteuclid.org/euclid.pja/1148392681

zbMATH Keywords

Bessel functions of representationslocal functional equations of Jacquet-LanglandsMean values of zeta-functionsGamma-functions of representations

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Zeta functions and (L)-functions of number fields (11R42)

Related Items (13)

On Motohashi’s formula ⋮ A note on the mean value of the zeta and \(L\)-functions. XIV ⋮ Higher moments of certain \(L\)-functions on the critical line ⋮ On the Fourier transform of Bessel functions over complex numbers. I: The spherical case ⋮ A Vorono\xEF–Oppenheim summation formula for number fields ⋮ A kernel formula for the action of the Weyl element in the Kirillov model of \(\mathrm{SL}(2,\mathbb{C})\) ⋮ The spectral decomposition of shifted convolution sums over number fields ⋮ Bessel identities in the Waldspurger correspondence over the complex numbers ⋮ On the Fourier transform of Bessel functions over complex numbers—II: The general case ⋮ Voronoi summation formula for Gaussian integers ⋮ A Whittaker-Plancherel inversion formula for \(\mathrm{SL}_2(\mathbb{C} )\) ⋮ On the Waldspurger formula and the metaplectic Ramanujan conjecture over number fields ⋮ A SEMI-ADELIC KUZNETSOV FORMULA OVER NUMBER FIELDS

Cites Work

• A note on the mean value of the zeta and \(L\)-functions. X.
• Whittaker vectors and conical vectors
• A note on the mean value of the zeta and \(L\)-functions. XII.
• Sum formula for Kloosterman sums and fourth moment of the Dedekind zeta-function over the Gaussian number field
• Automorphic forms on GL (2)
• Unnamed Item
• Unnamed Item

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