P Adic Aspects Of Modular Forms
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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). Contents:An Overview of Serre's p-Adic Modular Forms (Miljan Brakočević and R Sujatha)p-Adic Families of Ordinary Siegel Cusp Forms (Jacques Tilouine)Ordinary Families of Automorphic Forms on Definite Unitary Groups (Baskar Balasubramanyam and Dipramit Majumdar)Notes on Modularity Lifting in the Ordinary Case (David Geraghty)p-Adic L-Functions for Hilbert Modular Forms (Mladen Dimitrov)Arithmetic of Adjoint L-Values (Haruzo Hida)p-Adic L-Functions for GLn (Debargha Banerjee and A Raghuram)Non-Triviality of Generalised Heegner Cycles Over Anticyclotomic Towers: A Survey (Ashay A Burungale)The Euler System of Heegner Points and p-Adic L-Functions (Ming-Lun Hsieh)Non-Commutative q-Expansions (Mahesh Kakde) Readership: Researchers in algebra and number theory.
Hilbert Modular Forms Mod P And P Adic Aspects
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Author : Fabrizio Andreatta
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Hilbert Modular Forms Mod P And P Adic Aspects written by Fabrizio Andreatta 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 2005 with Mathematics categories.
We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$ theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we define operators $U$, $V$ and $\Theta_\chi$ and study the variation of the filtration under these operators. Our methods are geometric - comparing holomorphic Hilbert modular forms with rational functions on a moduli scheme with level-$p$ structure, whose poles are supported on the non-ordinary locus.In the $p$-adic theory we study congruences between Hilbert modular forms. This applies to the study of congruences between special values of zeta functions of totally real fields. It also allows us to define $p$-adic Hilbert modular forms 'a la Serre' as $p$-adic uniform limit of classical modular forms, and compare them with $p$-adic modular forms 'a la Katz' that are regular functions on a certain formal moduli scheme. We show that the two notions agree for cusp forms and for a suitable class of weights containing all the classical ones. We extend the operators $V$ and $\Theta_\chi$ to the $p$-adic setting.
Arithmetic Of P Adic Modular Forms
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Author : Fernando Q. Gouvea
language : en
Publisher: Springer
Release Date : 2006-11-14
Arithmetic Of P Adic Modular Forms written by Fernando Q. Gouvea and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.
Computations With Modular Forms
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Author : Gebhard Böckle
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-23
Computations With Modular Forms written by Gebhard Böckle 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 2014-01-23 with Mathematics categories.
This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.
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 Abelian varieties 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.
Arithmetic Of P Adic Modular Forms
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Author : Fernando Quadros Gouvêa
language : en
Publisher: Springer Verlag
Release Date : 1988
Arithmetic Of P Adic Modular Forms written by Fernando Quadros Gouvêa and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Introduction To Modular Forms
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Modular Forms written by Serge Lang 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.
From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#
Elliptic Curves Hilbert Modular Forms And Galois Deformations
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Author : Laurent Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-13
Elliptic Curves Hilbert Modular Forms And Galois Deformations written by Laurent Berger 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 2013-06-13 with Mathematics categories.
The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l ≠ p and local deformations at p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients. The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed. The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.
P Adic Numbers
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Author : Fernando Q. Gouvêa
language : en
Publisher: Springer Nature
Release Date : 2020-06-19
P Adic Numbers written by Fernando Q. Gouvêa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-19 with Mathematics categories.
There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE
The Web Of Modularity Arithmetic Of The Coefficients Of Modular Forms And Q Series
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Author : Ken Ono
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
The Web Of Modularity Arithmetic Of The Coefficients Of Modular Forms And Q Series written by Ken Ono 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 2004 with Mathematics categories.
Chapter 1.