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AuthorPanchishkin, Alexey A. author
TitleNon-Archimedean L-Functions of Siegel and Hilbert Modular Forms [electronic resource] / by Alexey A. Panchishkin
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991
Connect tohttp://dx.doi.org/10.1007/978-3-662-21541-8
Descript VII, 161 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Algebraic geometry Number theory Mathematics Number Theory Algebraic Geometry



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