Non-Archimedean L-Functions
of Siegel and Hilbert Modular Forms
Buch in deiner Nähe kaufen
Beschreibung
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.
1) p n=1 The set of arguments s for which ((s) is defined can be extended to all s E C,s :f:. 1, and we may regard C as the group of all continuous quasicharacters C = Hom(R~, c>
Autor*in
Alexei A. Panchishkin
Themen in »Non-Archimedean L-Functions«
11F 11R 11S 19K 46F 46G Eisenstein distributions analytic function convolution distribution measures modular forms zeta function
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From the reviews of the second edition:
"The book is an updated version of the book ‘Non-Archimedean L-Functions of Hilbert and Siegel Modular Forms’ by Alexei Panchishkin published in 1991 … . The main subject of the book is the p-adic theory of L-functions of Siegel modular forms. … The basic new feature of this second version is the use of arithmetical nearly holomorphic Siegel modular forms … . The book will be very useful for postgraduate students and researchers entering this difficult area of research." (Andrzej Dabrowski, Zentralblatt MATH, Vol. 1070, 2005)
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