Non-archimedean L-functions of Siegel and Hilbert modular forms / / Alexey A. Panchishkin

• Autore: Pančiškin A. A (Aleksej Alekseevič)
• Pubblicazione: Berlin ; ; Heidelberg : , : Springer-Verlag GmbH, , 1991
• Edizione: 1st ed. 1991.
• Descrizione fisica: 1 online resource (VII, 161 p.)
• Disciplina: 512.73
• Soggetto topico: L-functions; Siegel domains; Hilbert modular surfaces
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Content -- Acknowledgement -- 1. Non-Archimedean analytic functions, measures and distributions -- 2. Siegel modular forms and the holomorphic projection operator -- 3. Non-Archimedean standard zeta functions of Siegel modular forms -- 4. Non-Archimedean convolutions of Hilbert modular forms -- References.
• Sommario/riassunto: This book is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth (which were first introduced by Amice, Velu and Vishik in the elliptic modular case when they come from a good super singular reduction of elliptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a rapidly developing domain of algebraic number theory: the arithmetical theory of L-functions and modular forms.
• Titolo autorizzato: Non-archimedean L-functions of Siegel and Hilbert modular forms
• ISBN: 3-662-21541-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466595503316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture notes in mathematics (Springer-Verlag) ; ; 1471.