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|a 9783662215418
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|a Panchishkin, Alexei A.
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|a Non-Archimedean L-Functions
|h Elektronische Ressource
|b of Siegel and Hilbert Modular Forms
|c by Alexei A. Panchishkin
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| 250 |
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|a 1st ed. 1991
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1991, 1991
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| 300 |
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|a VII, 161 p
|b online resource
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| 505 |
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|a 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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| 653 |
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|a Algebraic Geometry
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| 653 |
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|a Number theory
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| 653 |
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|a Number Theory
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| 653 |
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|a Algebraic geometry
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Lecture Notes in Mathematics
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| 856 |
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|u https://doi.org/10.1007/978-3-662-21541-8?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 512.7
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| 520 |
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|a 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 supersingular reduction of ellptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arihmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a rapidly developping domain of algebraic number theory: the arithmetical theory of L-functions and modular forms
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