An Invitation To Q Series

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An Invitation To Q Series

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Author : Hei-Chi Chan
language : en
Publisher: World Scientific
Release Date : 2011

An Invitation To Q Series 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 with Mathematics categories.

The aim of this 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:
Release Date : 2011

An Invitation To Q Series written by Chan Hei-Chi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with q-series categories.

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 The Rogers Ramanujan Identities

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Author : Andrew V. Sills
language : en
Publisher: CRC Press
Release Date : 2017-10-16

An Invitation To The Rogers Ramanujan Identities written by Andrew V. Sills and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-16 with Mathematics categories.

The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.

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.

Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt

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Author : George E Andrews
language : en
Publisher: World Scientific
Release Date : 2024-08-19

Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt written by George E Andrews and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-19 with Mathematics categories.

This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.

Problems In The Theory Of Modular Forms

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Author : M. Ram Murty
language : en
Publisher: Springer
Release Date : 2016-11-25

Problems In The Theory Of Modular Forms written by M. Ram Murty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Mathematics categories.

This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.

Icp Case Series

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Author : Inter-university Case Program
language : en
Publisher:
Release Date : 1951

Icp Case Series written by Inter-university Case Program and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1951 with Public administration categories.

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.

Federal Register

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Author :
language : en
Publisher:
Release Date : 1955-08

Federal Register written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955-08 with Administrative law categories.