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Record Nr. |
UNISA996466655903316 |
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Autore |
Courtieu Michel <1973-> |
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Titolo |
Non-Archimedean L-functions and arithmetical Siegel modular forms / / Michel Courtieu, Alexei Panchishkin |
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Pubbl/distr/stampa |
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Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [2003] |
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©2003 |
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ISBN |
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Edizione |
[Second edition.] |
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Descrizione fisica |
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1 online resource (VIII, 204 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1471 |
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Classificazione |
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Disciplina |
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Soggetti |
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L-functions |
Siegel domains |
Modular groups |
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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 contenuto |
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Introduction -- Non-Archimedean analytic functions, measures and distributions -- Siegel modular forms and the holomorphic projection operator -- Arithmetical differential operators on nearly holomorphic Siegel modular forms -- Admissible measures for standard L-functions and nearly holomorphic Siegel modular forms. |
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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 |
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