On P Adic L Functions For Hilbert Modular Forms
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On P Adic L Functions For Hilbert Modular Forms
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Author : John Bergdall
language : en
Publisher:
Release Date : 2024
On P Adic L Functions For Hilbert Modular Forms written by John Bergdall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Automorphic forms categories.
On P Adic L Functions For Hilbert Modular Forms
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Author : John Bergdall
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-25
On P Adic L Functions For Hilbert Modular Forms written by John Bergdall and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-25 with Mathematics categories.
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P Adic Aspects Of Modular Forms
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Author : Baskar Balasubramanyam
language : en
Publisher: World Scientific
Release Date : 2016-06-14
P Adic Aspects Of Modular Forms written by Baskar Balasubramanyam and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-14 with Mathematics categories.
The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems. We finally consider p-adic L-functions for GL(2), the p-adic adjoint L-functions and some cases of higher GL(n).
Lectures On Hilbert Modular Varieties And Modular Forms
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Author : Eyal Zvi Goren
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Lectures On Hilbert Modular Varieties And Modular Forms written by Eyal Zvi Goren and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book is devoted to certain aspects of the theory of $p$-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of $p$-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelianvarieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of $p$-adic Hilbert modular forms and the geometry ofmoduli spaces of abelian varieties are related. This relation is used to study $q$-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-experts. It attempts to provide the necessary background to all concepts exposed in it. It may serve as a textbook for an advanced graduate course.
Hilbert Modular Forms And Iwasawa Theory
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Author : Haruzo Hida
language : en
Publisher: Clarendon Press
Release Date : 2006-06-15
Hilbert Modular Forms And Iwasawa Theory written by Haruzo Hida and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-15 with Mathematics categories.
The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.
Non Archimedean L Functions And Arithmetical Siegel Modular Forms
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Author : Michel Courtieu
language : en
Publisher: Springer
Release Date : 2003-12-09
Non Archimedean L Functions And Arithmetical Siegel Modular Forms written by Michel Courtieu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-09 with Mathematics categories.
This book, now in its 2nd edition, 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. The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book will be very useful for postgraduate students and for non-experts looking for a quick approach to a rapidly developing domain of algebraic number theory. This new edition is substantially revised to account for the new explanations that have emerged in the past 10 years of the main formulas for special L-values in terms of arithmetical theory of nearly holomorphic modular forms.
P Adic Automorphic Forms On Shimura Varieties
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Author : Haruzo Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
P Adic Automorphic Forms On Shimura Varieties written by Haruzo Hida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the early years of the 1980s, while I was visiting the Institute for Ad vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon ical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via L-functions and Eisenstein series (for which I visited lAS). Although it took more than 15 years, we now know (at least conjecturally) the exact number of variables for a given G, and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds (in a markedly different way). When I was asked to give a series of lectures in the Automorphic Semester in the year 2000 at the Emile Borel Center (Centre Emile Borel) at the Poincare Institute in Paris, I chose to give an exposition of the theory of p-adic (ordinary) families of such automorphic forms p-adic analytically de pending on their weights, and this book is the outgrowth of the lectures given there.
Convolutions Of Hilbert Modular Forms Motives And P Adic L Functions
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Author : A. A. Pančiškin
language : de
Publisher:
Release Date : 1990
Convolutions Of Hilbert Modular Forms Motives And P Adic L Functions written by A. A. Pančiškin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Iwasawa Theory And Its Perspective Volume 2
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Author : Tadashi Ochiai
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-25
Iwasawa Theory And Its Perspective Volume 2 written by Tadashi Ochiai and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-25 with Mathematics categories.
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.
P Adic L Functions And P Adic Representations
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Author : Bernadette Perrin-Riou
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
P Adic L Functions And P Adic Representations written by Bernadette Perrin-Riou and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Traditionally, p-adic L-functions have been constructed from complex L-functions via special values and Iwasawa theory. In this volume, Perrin-Riou presents a theory of p-adic L-functions coming directly from p-adic Galois representations (or, more generally, from motives). This theory encompasses, in particular, a construction of the module of p-adic L-functions via the arithmetic theory and a conjectural definition of the p-adic L-function via its special values. Since the original publication of this book in French (see Astérisque 229, 1995), the field has undergone significant progress. These advances are noted in this English edition. Also, some minor improvements have been made to the text.