Non-Archimedean L-functions of Siegel and Hilbert modular forms / Alexey A. Panchishkin
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1471Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1991ISBN: 9783662215418.ISSN: 1617-9692.Sujet MSC : 11F85, Discontinuous groups and automorphic forms, p-adic theory, local fields11S40, Algebraic number theory: local and p-adic fields, Zeta functions and L-functions
11F66, Discontinuous groups and automorphic forms, Langlands L-functions; one variable Dirichlet series and functional equations
11S80, Algebraic number theory: local and p-adic fields, Other analytic theory
11F41, Discontinuous groups and automorphic forms, Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfacesEn-ligne : Springerlink | Zentralblatt | MathSciNet
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Using the method of p-adic integration and of Rankin convolutions the author gives in great detail a construction of the p-adic L-functions attached to the standard zeta functions of Siegel modular forms and to the Rankin convolutions of Hilbert modular forms. In addition, a lot of background information is given on p-adic functions (p-adic measures, p- adic Mellin transforms etc.) and on Siegel- and Hilbert modular forms (theta series, Siegel-Eisenstein series, Hecke operators etc.); therefore the book should be accessible also to non-experts in the field. (Zentralblatt)
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