Invitation To Q Series An From Jacobi S Triple Product Identity To Ramanujan S Most Beautiful Identity
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Invitation To Q Series An From Jacobi S Triple Product Identity To Ramanujan S Most Beautiful Identity
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Author : Hei-chi Chan
language : en
Publisher: World Scientific
Release Date : 2011-04-04
Invitation To Q Series An From Jacobi S Triple Product Identity To Ramanujan S Most Beautiful Identity written by Hei-chi Chan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-04 with Mathematics categories.
The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G. H. Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.
An Invitation To Q Series
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Author : Chan Hei-Chi
language : en
Publisher: World Scientific
Release Date : 2011
An Invitation To Q Series written by Chan Hei-Chi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the RogersOCoRamanujan continued fraction OCo a result that convinced G H Hardy that Ramanujan was a OC mathematician of the highest classOCO, and (2) what G. H. Hardy called Ramanujan''s OC Most Beautiful IdentityOCO. This book covers a range of related results, such as several proofs of the famous RogersOCoRamanujan identities and a detailed account of Ramanujan''s congruences. It also covers a range of techniques in q-series."
Theta Functions Elliptic Functions And
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Author : Heng Huat Chan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-07-06
Theta Functions Elliptic Functions And written by Heng Huat Chan and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-06 with Mathematics categories.
This book presents several results on elliptic functions and Pi, using Jacobi’s triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan’s work on Pi. The included exercises make it ideal for both classroom use and self-study.
The Power Of Q
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Author : Michael D. Hirschhorn
language : en
Publisher: Springer
Release Date : 2017-08-08
The Power Of Q written by Michael D. Hirschhorn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-08 with Mathematics categories.
This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and life-long study—inspired by Ramanujan—of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange’s four-squares theorem and Gauss’s two-squares theorem. Attention then turns to partitions and Ramanujan’s partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction, the famous “forty identities” of Ramanujan, and the representation results of Jacobi, Dirichlet and Lorenz, not to mention many other interesting and beautiful results. We also meet a challenge of D.H. Lehmer to give a formula for the number of partitions of a number into four squares, prove a “mysterious” partition theorem of H. Farkas and prove a conjecture of R.Wm. Gosper “which even Erdős couldn’t do.” The book concludes with a look at Ramanujan’s remarkable tau function.
My Mathematical Universe People Personalities And The Profession
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Author : Krishnaswami Alladi
language : en
Publisher: World Scientific
Release Date : 2022-11-15
My Mathematical Universe People Personalities And The Profession written by Krishnaswami Alladi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-15 with Mathematics categories.
This is an autobiography and an exposition on the contributions and personalities of many of the leading researchers in mathematics and physics with whom Dr Krishna Alladi, Professor of Mathematics at the University of Florida, has had personal interaction with for over six decades. Discussions of various aspects of the physics and mathematics academic professions are included.Part I begins with the author's unusual and frequent introductions as a young boy to scientific luminaries like Nobel Laureates Niels Bohr, Murray Gell-Mann, and Richard Feynman, in the company of his father, the scientist Alladi Ramakrishnan. Also in Part I is an exciting account of how the author started his research investigations in number theory as an undergraduate, and how contact and collaboration with the great Paul Erdős as a student influenced him in his career.In-depth views of the Institute for Advanced Study, Princeton, and several major American Universities are given, and fascinating descriptions of the work and personalities of some Field Medalists and eminent mathematicians are provided.Part II deals with the author's tenure at the University of Florida where he initiated several programs as Mathematics Chair for a decade, and how he has served the profession in various capacities, most notably as Chair of the SASTRA Ramanujan Prize Committee and Editor-in-Chief of The Ramanujan Journal.The book would appeal to academicians and the general public, since the author has blended academic and scientific discussions at a non-technical level with descriptions of destinations in his international travels for work and pleasure. The reader is invited to dig as deep as desired and is guaranteed to be treated to whimsical stories and personal peeks at some of the great luminaries of the twentieth and twenty-first centuries.
Ramanujan S Lost Notebook
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Author : George E. Andrews
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-06
Ramanujan S Lost Notebook written by George E. Andrews 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 2005-05-06 with Biography & Autobiography categories.
In the library at Trinity College, Cambridge in 1976, George Andrews of Pennsylvania State University discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. Soon designated as "Ramanujan’s Lost Notebook," it contains considerable material on mock theta functions and undoubtedly dates from the last year of Ramanujan’s life. In this book, the notebook is presented with additional material and expert commentary.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1999-11
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11 with Mathematics categories.
Integer Partitions
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Author : George E. Andrews
language : en
Publisher: Cambridge University Press
Release Date : 2004-10-11
Integer Partitions written by George E. Andrews 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 2004-10-11 with Mathematics categories.
Provides a wide ranging introduction to partitions, accessible to any reader familiar with polynomials and infinite series.
Number Theory In The Spirit Of Ramanujan
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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Number Theory In The Spirit Of Ramanujan written by Bruce C. Berndt 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 2006 with Mathematics categories.
Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.
My Search For Ramanujan
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Author : Ken Ono
language : en
Publisher: Springer
Release Date : 2016-04-20
My Search For Ramanujan written by Ken Ono and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-20 with Mathematics categories.
"The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics. Ono describes his rocky path through college and graduate school, interweaving Ramanujan’s story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan’s mathematical legacy. Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents. Ono’s search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity."