Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms
Panchishkin, Alexey A.
Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms [electronic resource] / by Alexey A. Panchishkin. - VII, 161 p. online resource. - Lecture Notes in Mathematics, 1471 0075-8434 ; . - Lecture Notes in Mathematics, 1471 .
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.
9783662215418
10.1007/978-3-662-21541-8 doi
Number theory.
Geometry, algebraic.
Number Theory.
Algebraic Geometry.
QA241-247.5
512.7
Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms [electronic resource] / by Alexey A. Panchishkin. - VII, 161 p. online resource. - Lecture Notes in Mathematics, 1471 0075-8434 ; . - Lecture Notes in Mathematics, 1471 .
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.
9783662215418
10.1007/978-3-662-21541-8 doi
Number theory.
Geometry, algebraic.
Number Theory.
Algebraic Geometry.
QA241-247.5
512.7