 Aptly conveys the beauty and power of qseries
 Accessible to advanced undergraduates, graduate students, and researchers
 Historical notes enrich the readers understanding of the subject
 First monograph to focus uniquely on qseries
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 About this book

This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and lifelong 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 qseries is demonstrated with proofs of Lagrange’s foursquares theorem and Gauss’s twosquares 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.
 Reviews

“This book provides an introduction to qseries that would be accessible to calculus students, its main purpose is to offer beautiful theorems to the reader along with, in many instances, equally beautiful proofs that cannot be found elsewhere, except possibly in the author’s own papers. … those who already love qseries will find much to admire and enjoy in Hirschhorn’s book The Power of q. Those desiring an introduction to the subject can also enjoy it.” (Bruce Berndt, The American Mathematical Monthly, Vol. 126 (2), April, 2019)
 Table of contents (44 chapters)


Introduction
Pages 117

Jacobi’s TwoSquares and FourSquares Theorems
Pages 1926

Ramanujan’s Partition Congruences
Pages 2742

Ramanujan’s Partition Congruences—A Uniform Proof
Pages 4354

Ramanujan’s Most Beautiful Identity
Pages 5558

Table of contents (44 chapters)
 Download Preface 1 PDF (77.4 KB)
 Download Sample pages 2 PDF (113 KB)
 Download Table of contents PDF (406.4 KB)
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Bibliographic Information
 Bibliographic Information

 Book Title
 The Power of q
 Book Subtitle
 A Personal Journey
 Authors

 Michael D. Hirschhorn
 Series Title
 Developments in Mathematics
 Series Volume
 49
 Copyright
 2017
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing AG
 eBook ISBN
 9783319577623
 DOI
 10.1007/9783319577623
 Hardcover ISBN
 9783319577616
 Softcover ISBN
 9783319862415
 Series ISSN
 13892177
 Edition Number
 1
 Number of Pages
 XXIV, 415
 Topics