The 1 2 3 Of Modular Forms
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The 1 2 3 Of Modular Forms
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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2009-09-02
The 1 2 3 Of Modular Forms written by Jan Hendrik Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
The 1 2 3 Of Modular Forms
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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-10
The 1 2 3 Of Modular Forms written by Jan Hendrik Bruinier 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 2008-02-10 with Mathematics categories.
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Modular Forms Basics And Beyond
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Author : Goro Shimura
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-18
Modular Forms Basics And Beyond written by Goro Shimura 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 2011-11-18 with Mathematics categories.
This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically.
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#
Introduction To Elliptic Curves And Modular Forms
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Author : Neal I. Koblitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Elliptic Curves And Modular Forms written by Neal I. Koblitz 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.
This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses. thereby solidifying their under standing of some basic tools used throughout mathematics. Graduate stu dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under graduates could use the book for independent study projects, senior theses, and seminar work.
Heads In Grammatical Theory
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Author : Greville G. Corbett
language : en
Publisher: Cambridge University Press
Release Date : 1993-06-24
Heads In Grammatical Theory written by Greville G. Corbett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-24 with Language Arts & Disciplines categories.
A study of the idea of the 'head' or dominating element of a phrase.
Modular Forms A Computational Approach
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Author : William A. Stein
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-02-13
Modular Forms A Computational Approach written by William A. Stein 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 2007-02-13 with Mathematics categories.
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.
From Number Theory To Physics
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Author : Michel Waldschmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
From Number Theory To Physics written by Michel Waldschmidt 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 2013-03-09 with Science categories.
The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theoryand Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch.
Modular Forms A Classical And Computational Introduction 2nd Edition
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Author : Lloyd James Peter Kilford
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-03-12
Modular Forms A Classical And Computational Introduction 2nd Edition written by Lloyd James Peter Kilford and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Mathematics categories.
Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.