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Item Details
| Title:
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THE POWER OF Q
A PERSONAL JOURNEY |
| By: |
Michael D. Hirschhorn |
| Format: |
Hardback |
| List price:
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£109.99 |
| Our price: |
£98.99 |
| Discount: |
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| You save:
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£11.00 |
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| 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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