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Record Nr. |
UNISA996466595503316 |
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Autore |
Pančiškin A. A (Aleksej Alekseevič) |
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Titolo |
Non-archimedean L-functions of Siegel and Hilbert modular forms / / Alexey A. Panchishkin |
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Pubbl/distr/stampa |
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Berlin ; ; Heidelberg : , : Springer-Verlag GmbH, , 1991 |
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ISBN |
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Edizione |
[1st ed. 1991.] |
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Descrizione fisica |
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1 online resource (VII, 161 p.) |
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Collana |
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Lecture notes in mathematics ; ; 1471 |
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Disciplina |
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Soggetti |
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L-functions |
Siegel domains |
Hilbert modular surfaces |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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. |
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