Special values of zeta functions attached to Siegel modular forms

DOI10.24033/asens.1398zbMath0465.10022OpenAlexW2598147392MaRDI QIDQ3916638

Michael Harris

Publication date: 1981

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1981_4_14_1_77_0

zbMATH Keywords

Dirichlet seriesSiegel modular formsarithmetic properties

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67)

Related Items

The special values of the standard 𝐿-functions for 𝐺𝑆𝑝_{2𝑛}×𝐺𝐿₁, Some remarks on triple L-functions, Differential operators and families of automorphic forms on unitary groups of arbitrary signature, Power series expansions of modular forms and p-adic interpolation of the square roots of Rankin–Selberg special values, Unnamed Item, On integrality of Eisenstein liftings, On algebraicity of special values of symmetric 4-th and 6-th power \(L\)-functions for \(\operatorname{GL}(2)\), Congruences for Hecke eigenvalues of Siegel modular forms, The rationality of holomorphic Eisenstein series, Maass operators and Eisenstein series, Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of \(p\)-adic \(L\)-functions, \(p\)-adic differential operators on automorphic forms on unitary groups, A \(p\)-adic Maass-Shimura operator on Mumford curves, Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen, On Eisenstein series for Siegel modular groups. II, -ADIC -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS, POWER SERIES EXPANSIONS OF MODULAR FORMS AND THEIR INTERPOLATION PROPERTIES, On the arithmetic of Siegel-Hilbert cusp forms: Petersson inner products and Fourier coefficients, Differential operators mod \(p\): analytic continuation and consequences, On the Siegel-Eisenstein measure and its applications, Arithmeticity of holomorphic cuspforms on Hermitian symmetric domains, On the standard \(L\)-function for \(\mathrm{GSp}_{2n}\times\mathrm{GL}_1\) and algebraicity of symmetric fourth \(L\)-values for \(\mathrm{GL}_2\), Unnamed Item, Poles and residues of standard L-functions attached to Siegel modular forms, Unnamed Item, Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen. II, An introduction to Eisenstein measures, Special values of L-functions for Saito–Kurokawa lifts, \(p\)-adic measures attached to Siegel modular forms, On the degree five $L$-function for $\mathrm {GSp}(4)$, On special values of standard \(L\)-functions attached to vector valued Siegel modular forms., Congruences for Fourier coefficients of lifted Siegel modular forms. I: Eisenstein lifts, On differential operators and congruences for Siegel modular forms of degree two, On certain vector valued Siegel modular forms of degree two, On Special L-Values Attached to Siegel Modular Forms, The weight reduction of mod \(p\) Siegel modular forms for \(GSp_4\) and theta operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(p\)-adic \(L\)-functions for CM fields
• Symmetric squares of zeta-functions of Siegel modular forms of genus 2
• A note on three lemmas of Shimura
• Restrictions and expansions of holomorphic representations
• The rationality of holomorphic Eisenstein series
• Singular holomorphic representations and singular modular forms
• Automorphic forms of singular weight are singular forms
• Holomorphe Differentialformen zu Kongruenzgruppen der Siegelschen Modulgruppe
• On some arithmetic properties of modular forms of one and several variables
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• On the periods of modular forms
• On the derivatives of theta functions and modular forms
• The special values of the zeta functions associated with Hilbert modular forms
• On certain reciprocity-laws for theta functions and modular forms
• Algebraic solutions of differential equations (p-curvature and the Hodge filtration)
• On the theory of \(\vartheta\)-functions, the moduli of Abelian varieties, and the moduli of curves
• Compactification of arithmetic quotients of bounded symmetric domains
• On the differentiation of De Rham cohomology classes with respect to parameters
• Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars.
• On certain square-integrable irreducible unitary representations of some p-adic linear groups
• Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen
• Siegel's modular forms and Dirichlet series. Course given at the University of Maryland, 1969-1970
• Theory of spherical functions on reductive algebraic groups over p-adic fields
• Einführung in die Theorie der Modulfunktionen \(n\)-ten Grades
• Die Differentialgleichungen in der Theorie der Siegelschen Modulfunktionen. (The differential equations in the theory of Siegel's modular functions)
• Representations of Semisimple Lie Groups, V
• THE MULTIPLICATIVE ARITHMETIC OR SIEGEL MODULAR FORMS
• Special Values of Zeta Functions, and Eisenstein Series of Half Integral Weight
• The special values of the zeta functions associated with cusp forms
• ON FACTORIZATION OF HECKE POLYNOMIALS FOR THE SYMPLECTIC GROUP OF GENUS $ n$
• Intertwining Differential Operators for Mp(n, R) and SU(n, n)
• EULER EXPANSIONS OF THETA-TRANSFORMS OF SIEGEL MODULAR FORMS OF DEGREE $ n$
• Symplectic Geometry
• Travaux de Shimura
• On the De Rham cohomology of algebraic varieties