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Author : Jacobus Hendricus van Lint
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (26 download)
Download or read book Hecke Operators and Euler Products written by Jacobus Hendricus van Lint and published by . This book was released on 1957 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : V. S. Varadarajan
Publisher : American Mathematical Soc.
ISBN 13 : 0821835807
Total Pages : 312 pages
Book Rating : 4.8/5 (218 download)
Download or read book Euler Through Time written by V. S. Varadarajan and published by American Mathematical Soc.. This book was released on 2006 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euler is one of the greatest and most prolific mathematicians of all time. He wrote the first accessible books on calculus, created the theory of circular functions, and discovered new areas of research such as elliptic integrals, the calculus of variations, graph theory, divergent series, and so on. It took hundreds of years for his successors to develop in full the theories he began, and some of his themes are still at the center of today's mathematics. It is of great interesttherefore to examine his work and its relation to current mathematics. This book attempts to do that. In number theory the discoveries he made empirically would require for their eventual understanding such sophisticated developments as the reciprocity laws and class field theory. His pioneering work onelliptic integrals is the precursor of the modern theory of abelian functions and abelian integrals. His evaluation of zeta and multizeta values is not only a fantastic and exciting story but very relevant to us, because they are at the confluence of much research in algebraic geometry and number theory today (Chapters 2 and 3 of the book). Anticipating his successors by more than a century, Euler created a theory of summation of series that do not converge in the traditional manner. Chapter 5of the book treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics. The last chapter contains a brief treatment of Euler products. Euler discovered the product formula over the primes for the zeta function as well as for a smallnumber of what are now called Dirichlet $L$-functions. Here the book goes into the development of the theory of such Euler products and the role they play in number theory, thus offering the reader a glimpse of current developments (the Langlands program).
Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1108709451
Total Pages : 779 pages
Book Rating : 4.1/5 (87 download)
Download or read book Series and Products in the Development of Mathematics written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page 779 pages. Available in PDF, EPUB and Kindle. Book excerpt: First of two volumes tracing the development of series and products. Second edition adds extensive material from original works.
Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1108573150
Total Pages : 480 pages
Book Rating : 4.1/5 (85 download)
Download or read book Series and Products in the Development of Mathematics: Volume 2 written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.
Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1108573185
Total Pages : pages
Book Rating : 4.1/5 (85 download)
Download or read book Series and Products in the Development of Mathematics: Volume 1 written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.
Author : Canadian Number Theory Association. Conference
Publisher : American Mathematical Soc.
ISBN 13 : 9780821803127
Total Pages : 460 pages
Book Rating : 4.8/5 (31 download)
Download or read book Number Theory written by Canadian Number Theory Association. Conference and published by American Mathematical Soc.. This book was released on 1995 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains proceedings presented at the fourth Canadian Number Theory Association conference held at Dalhousie University in July 1994. The invited speakers focused on analytic, algebraic, and computational number theory. The contributed talks represented a wide variety of areas in number theory.
Author : Anthony W. Knapp
Publisher : Princeton University Press
ISBN 13 : 0691186901
Total Pages : 444 pages
Book Rating : 4.6/5 (911 download)
Download or read book Elliptic Curves. (MN-40), Volume 40 written by Anthony W. Knapp and published by Princeton University Press. This book was released on 2018-06-05 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner.
Author : Library of Congress
Publisher :
ISBN 13 :
Total Pages : 1556 pages
Book Rating : 4.3/5 (243 download)
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 1989 with total page 1556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Library of Congress. Subject Cataloging Division
Publisher :
ISBN 13 :
Total Pages : 1546 pages
Book Rating : 4.3/5 (91 download)
Download or read book Library of Congress Subject Headings: P-Z written by Library of Congress. Subject Cataloging Division and published by . This book was released on 1989 with total page 1546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Library of Congress. Cataloging Policy and Support Office
Publisher :
ISBN 13 :
Total Pages : 1032 pages
Book Rating : 4.3/5 (91 download)
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2006 with total page 1032 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Library of Congress. Subject Cataloging Division
Publisher :
ISBN 13 :
Total Pages : 1452 pages
Book Rating : 4.:/5 (31 download)
Download or read book Library of Congress Subject Headings: F-O written by Library of Congress. Subject Cataloging Division and published by . This book was released on 1988 with total page 1452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 038749894X
Total Pages : 619 pages
Book Rating : 4.3/5 (874 download)
Download or read book Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2008-12-17 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.
Author : George W. Mackey
Publisher : American Mathematical Soc.
ISBN 13 : 9780821890448
Total Pages : 386 pages
Book Rating : 4.8/5 (94 download)
Download or read book The Scope and History of Commutative and Noncommutative Harmonic Analysis written by George W. Mackey and published by American Mathematical Soc.. This book was released on 2005-04-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: ''When I was invited to speak at the conference on the history of analysis given at Rice University [in 1977], I decided that it might be interesting to review the history of mathematics and physics in the last three hundred years or so with heavy emphasis on those parts in which harmonic analysis had played a decisive or at least a major role. I was pleased and somewhat astonished to find how much of both subjects could be included under this rubric ... The picture that gradually emerged as the various details fell into place was one that I found very beautiful, and the process of seeing it do so left me in an almost constant state of euphoria. I would like to believe that others can be led to see this picture by reading my paper, and to facilitate this I have included a large number of short expositions of topics which are not widely understood by non-specialists.'' --from the Preface This volume, containing the paper mentioned above as well as five other reprinted papers by Mackey, presents a sweeping view of the importance, utility, and beauty of harmonic analysis and its connections to other areas of mathematics and science. A seventh paper, written exclusively for this volume, attempts to unify certain themes that emerged after major discoveries in 1967 and 1968 in the areas of Lie algebras, strong interaction physics, statistical mechanics, and nonlinear partial differential equations--discoveries that may at first glance appear to be independent, but which are in fact deeply interrelated. Information for our distributors: Copublished with the London Mathematical Society beginning with volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Author : Pierre Eymard
Publisher : Springer
ISBN 13 : 3540460322
Total Pages : 301 pages
Book Rating : 4.5/5 (44 download)
Download or read book Harmonic Analysis written by Pierre Eymard and published by Springer. This book was released on 2006-11-14 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George E. Andrews
Publisher : Springer
ISBN 13 : 331977834X
Total Pages : 433 pages
Book Rating : 4.3/5 (197 download)
Download or read book Ramanujan's Lost Notebook written by George E. Andrews and published by Springer. This book was released on 2018-09-05 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. Review from the second volume:"Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."- MathSciNet Review from the first volume:"Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."- Gazette of the Australian Mathematical Society
Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1107159385
Total Pages : 491 pages
Book Rating : 4.1/5 (71 download)
Download or read book Elliptic and Modular Functions from Gauss to Dedekind to Hecke written by Ranjan Roy and published by Cambridge University Press. This book was released on 2017-04-18 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.
Author : Dale Husemoller
Publisher : Springer Science & Business Media
ISBN 13 : 1475751192
Total Pages : 363 pages
Book Rating : 4.4/5 (757 download)
Download or read book Elliptic Curves written by Dale Husemoller and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respect to details of proofs. For example, the first part, to Chapter 6, is undergraduate in level, the second part requires a background in Galois theory and the third some complex analysis, while the last parts, from Chapter 12 on, are mostly at graduate level. A general outline ofmuch ofthe material can be found in Tate's colloquium lectures reproduced as an article in Inven tiones [1974]. The first part grew out of Tate's 1961 Haverford Philips Lectures as an attempt to write something for publication c10sely related to the original Tate notes which were more or less taken from the tape recording of the lectures themselves. This inc1udes parts of the Introduction and the first six chapters The aim ofthis part is to prove, by elementary methods, the Mordell theorem on the finite generation of the rational points on elliptic curves defined over the rational numbers. In 1970 Tate teturned to Haverford to give again, in revised form, the originallectures of 1961 and to extend the material so that it would be suitable for publication. This led to a broader plan forthe book.
