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Item Details
Title: THE POWER OF Q
A PERSONAL JOURNEY
By: Michael D. Hirschhorn
Format: Hardback

List price: £109.99
Our price: £98.99
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10% off
You save: £11.00
ISBN 10: 3319577611
ISBN 13: 9783319577616
Availability: Usually dispatched within 3-5 days.
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Stock: Currently 1item in stock
Publisher: SPRINGER INTERNATIONAL PUBLISHING AG
Pub. date: 3 August, 2017
Edition: 1st ed. 2017
Series: Developments in Mathematics 49
Pages: 415
Synopsis: This unique book explores the world of q, known technically as basic hypergeometricseries, and represents the author's personal and life-long study-inspired by Ramanujan-ofaspects of this broad topic. While the level of mathematical sophistication isgraduated, the book is designed to appeal to advanced undergraduates as well asresearchers in the field. The principal aims are to demonstrate the power of the methodsand the beauty of the results. The book contains novel proofs of many results in thetheory 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 coursework; it has many suitable exercises.After an introductory chapter, the power of q-series is demonstrated with proofs ofLagrange's four-squares theorem and Gauss's two-squares theorem. Attention thenturns to partitions and Ramanujan's partition congruences. Several proofs of these aregiven throughout the book. Many chapters are devoted to related and other associatedtopics. One highlight is a simple proof of an identity of Jacobi with application tostring theory. On the way, we come across the Rogers-Ramanujan identities and theRogers-Ramanujan continued fraction, the famous "forty identities" of Ramanujan, andthe representation results of Jacobi, Dirichlet and Lorenz, not to mention many otherinteresting and beautiful results. We also meet a challenge of D.H. Lehmer to give aformula 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 evenErdos couldn't do." The book concludes with a look at Ramanujan's remarkable taufunction.
Illustrations: XXII, 415 p.
Publication: Switzerland
Imprint: Springer International Publishing AG
Returns: Non-returnable
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