The critical values of certain Dirichlet series attached to Hilbert modular forms

DOI10.1215/S0012-7094-91-06324-6zbMath0752.11021OpenAlexW1591076190MaRDI QIDQ1180457

Goro Shimura

Publication date: 27 June 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06324-6

zbMATH Keywords

Hilbert modular formsinvariantDirichlet seriesHecke eigenform

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items

On the critical values of \(L\)-functions of \(GL(2)\) and \(GL(2)\times GL(2)\), On the zeta functions of Shimura varieties and periods of Hilbert modular forms, Eisenstein series and zeta functions on symplectic groups, Convergence of zeta functions on symplectic and metaplectic groups, Cohomology and \(L\)-values, On a theta correspondence with respect to a quadratic extension, Hecke Eigenvalues for Real Quadratic Fields, On the Fourier coefficients of Hilbert modular forms of half-integral weight, Euler products and Fourier coefficients of automorphic forms on symplectic groups, On adelic automorphic forms with respect to a quadratic extension

Cites Work

• On Eisenstein series
• On Eisenstein series of half-integral weight
• On the Eisenstein series of Hilbert modular groups
• Nearly holomorphic functions on Hermitian symmetric spaces
• On Hilbert modular forms of half-integral weight
• Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\)
• The arithmetic of certain zeta functions and automorphic forms on orthogonal groups
• The critical values of certain zeta functions associated with modular forms of half-integral weight
• On the periods of modular forms
• The special values of the zeta functions associated with Hilbert modular forms
• Evaluation of the Symmetric Square at the Near Center Point
• Algebraic Relations Between Critical Values of Zeta Functions and Inner Products
• Special Values of Zeta Functions, and Eisenstein Series of Half Integral Weight
• Addendum to Special Values of Zeta Functions
• Special Values of Dirichlet Series Attached to Hilbert Modular Forms
• On the Holomorphy of Certain Dirichlet Series
• The special values of the zeta functions associated with cusp forms