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Author : Fernando Q. Gouvea
Publisher :
ISBN 13 : 9783662193846
Total Pages : 132 pages
Book Rating : 4.1/5 (938 download)
Download or read book Arithmetic of P-Adic Modular Forms written by Fernando Q. Gouvea and published by . This book was released on 2014-09-01 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fernando Quadros Gouvêa
Publisher : Springer Verlag
ISBN 13 : 9780387189468
Total Pages : 121 pages
Book Rating : 4.1/5 (894 download)
Download or read book Arithmetic of P-adic Modular Forms written by Fernando Quadros Gouvêa and published by Springer Verlag. This book was released on 1988 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fernando Q. Gouvea
Publisher : Springer
ISBN 13 : 3540388540
Total Pages : 129 pages
Book Rating : 4.5/5 (43 download)
Download or read book Arithmetic of p-adic Modular Forms written by Fernando Q. Gouvea and published by Springer. This book was released on 2006-11-14 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Baskar Balasubramanyam
Publisher : World Scientific
ISBN 13 : 9814719242
Total Pages : 344 pages
Book Rating : 4.8/5 (147 download)
Download or read book p-Adic Aspects of Modular Forms written by Baskar Balasubramanyam and published by World Scientific. This book was released on 2016-06-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Haruzo Hida
Publisher : Springer Science & Business Media
ISBN 13 : 9780387207117
Total Pages : 414 pages
Book Rating : 4.2/5 (71 download)
Download or read book p-Adic Automorphic Forms on Shimura Varieties written by Haruzo Hida and published by Springer Science & Business Media. This book was released on 2004-05-10 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1. An elementary construction of Shimura varieties as moduli of abelian schemes. 2. p-adic deformation theory of automorphic forms on Shimura varieties. 3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety. The book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others). Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000).
Author : Fernando Q. Gouvêa
Publisher : Springer Nature
ISBN 13 : 3030472957
Total Pages : 366 pages
Book Rating : 4.0/5 (34 download)
Download or read book p-adic Numbers written by Fernando Q. Gouvêa and published by Springer Nature. This book was released on 2020-06-19 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Fabrizio Andreatta
Publisher : American Mathematical Soc.
ISBN 13 : 0821836099
Total Pages : 100 pages
Book Rating : 4.8/5 (218 download)
Download or read book Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects written by Fabrizio Andreatta and published by American Mathematical Soc.. This book was released on 2005 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Eyal Zvi Goren
Publisher : American Mathematical Soc.
ISBN 13 : 082181995X
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lectures on Hilbert Modular Varieties and Modular Forms written by Eyal Zvi Goren and published by American Mathematical Soc.. This book was released on 2002 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : William A. Stein
Publisher : American Mathematical Soc.
ISBN 13 : 0821839608
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)
Download or read book Modular Forms, a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Author : Laurent Berger
Publisher : Springer Science & Business Media
ISBN 13 : 3034806183
Total Pages : 249 pages
Book Rating : 4.0/5 (348 download)
Download or read book Elliptic Curves, Hilbert Modular Forms and Galois Deformations written by Laurent Berger and published by Springer Science & Business Media. This book was released on 2013-06-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Haruzo Hida
Publisher : Springer Science & Business Media
ISBN 13 : 1468493906
Total Pages : 397 pages
Book Rating : 4.4/5 (684 download)
Download or read book p-Adic Automorphic Forms on Shimura Varieties written by Haruzo Hida and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Fred Diamond
Publisher : Springer Science & Business Media
ISBN 13 : 0387272267
Total Pages : 450 pages
Book Rating : 4.3/5 (872 download)
Download or read book A First Course in Modular Forms written by Fred Diamond and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
Author : Gary Cornell
Publisher : Springer Science & Business Media
ISBN 13 : 1461219744
Total Pages : 592 pages
Book Rating : 4.4/5 (612 download)
Download or read book Modular Forms and Fermat’s Last Theorem written by Gary Cornell and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.
Author : Brian David Conrad
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886915
Total Pages : 588 pages
Book Rating : 4.8/5 (869 download)
Download or read book Arithmetic Algebraic Geometry written by Brian David Conrad and published by American Mathematical Soc.. This book was released on with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.
Author : Willem Kuyk
Publisher : Springer
ISBN 13 : 3540378022
Total Pages : 352 pages
Book Rating : 4.5/5 (43 download)
Download or read book Modular Functions of One Variable III written by Willem Kuyk and published by Springer. This book was released on 2009-02-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gebhard Böckle
Publisher : Springer Science & Business Media
ISBN 13 : 3319038478
Total Pages : 376 pages
Book Rating : 4.3/5 (19 download)
Download or read book Computations with Modular Forms written by Gebhard Böckle and published by Springer Science & Business Media. This book was released on 2014-01-23 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Donald G. Babbitt
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896709
Total Pages : 762 pages
Book Rating : 4.8/5 (967 download)
Download or read book Featured Reviews in Mathematical Reviews 1997-1999 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2000-05-05 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
