Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms [electronic resource] / by Alexey A. Panchishkin.
Material type: TextSeries: Lecture Notes in Mathematics, Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn — vol. 16 ; 1471Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991Description: VII, 161 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783662215418Subject(s): Mathematics | Geometry, algebraic | Number theory | Mathematics | Number Theory | Algebraic GeometryAdditional physical formats: Printed edition:: No titleDDC classification: 512.7 LOC classification: QA241-247.5Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK2030 |
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.
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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