Heads in Grammatical Theory
Author: Greville G. Corbett
Publisher: Cambridge University Press
Published: 1993-06-24
Total Pages: 364
ISBN-13: 9780521402453
DOWNLOAD EBOOK →A study of the idea of the 'head' or dominating element of a phrase.
Lanterna Rally
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Introduction to Modular Forms
Author: Serge Lang
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 267
ISBN-13: 3642514472
DOWNLOAD EBOOK →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#
The 1-2-3 of Modular Forms
Author: Jan Hendrik Bruinier
Publisher: Springer Science & Business Media
Published: 2008-02-10
Total Pages: 273
ISBN-13: 3540741194
DOWNLOAD EBOOK →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
Author: L J P Kilford
Publisher: World Scientific Publishing Company
Published: 2015-03-12
Total Pages: 252
ISBN-13: 1783265477
DOWNLOAD EBOOK →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.
Introduction to Elliptic Curves and Modular Forms
Author: Neal I. Koblitz
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 262
ISBN-13: 1461209099
DOWNLOAD EBOOK →The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.
Modular Forms, a Computational Approach
Author: William A. Stein
Publisher: American Mathematical Soc.
Published: 2007-02-13
Total Pages: 290
ISBN-13: 0821839608
DOWNLOAD EBOOK →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.
Modular Forms: A Classical Approach
Author: Henri Cohen
Publisher: American Mathematical Soc.
Published: 2017-08-02
Total Pages: 700
ISBN-13: 0821849476
DOWNLOAD EBOOK →The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.
Introduction to Applications of Modular Forms
Author: Zafer Selcuk Aygin
Publisher:
Published: 2023
Total Pages: 0
ISBN-13: 9783031326318
DOWNLOAD EBOOK →This book is a self-contained treatment for those who study or work on the computational aspects of classical modular forms. The author describes the theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the theory in context and make new conjectures. In addition, this book: Describes the theory of modular forms and its applications in number theoretic problems Provides a resource for people who study or work on the computational aspects of classical modular forms Includes computer algorithms to help readers conjecture new results and prove them using the presented theory.
A First Course in Modular Forms
Author: Fred Diamond
Publisher: Springer Science & Business Media
Published: 2006-03-30
Total Pages: 450
ISBN-13: 0387272267
DOWNLOAD EBOOK →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.
Introduction to Applications of Modular Forms
Author: Zafer Selcuk Aygin
Publisher: Springer Nature
Published: 2023-07-13
Total Pages: 175
ISBN-13: 3031326296
DOWNLOAD EBOOK →This book is a self-contained treatment for those who study or work on the computational aspects of classical modular forms. The author describes the theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the theory in context and make new conjectures.
