The Power of q A Personal Journey /

• Κύριος συγγραφέας: Hirschhorn, Michael D. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Σειρά: Developments in Mathematics, 49
• Θέματα: Mathematics.; Number theory.; Number Theory.

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 ad...

Πίνακας περιεχομένων:

• Foreword
• Preface
• 1. Introduction
• 2. Jacobi's two-squares and four-squares theorems
• 3. Ramanujan's partition congruences
• 4. Ramanujan's partition congruences— a uniform proof
• 5. Ramanujan's "most beautiful identity"
• 6. Ramanujan's partition congruences for powers of 5
• 7. Ramanujan's partition congruences for powers of 7
• 8. Ramanujan's 5-dissection of Euler's product
• 9. A "difficult and deep" identity of Ramanujan
• 10. The quintuple product identity
• 11. Winquist's identity
• 12. The crank of a partition
• 13. Two more proofs of p(11n + 6) ≡ 0 (mod 11), and more
• 14. Partitions where even parts come in two colours
• 15. The Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction
• 16. The series expansion of the Rogers–Ramanujan continued fraction
• 17. The 2- and 4-dissections of Ramanujan’s continued fraction and its reciprocal
• 18. The series expansion of the Ramanujan-Gollnitz-Gordon continued fraction and its reciprocal
• 19. Jacobi’s “aequatio identica satis abstrusa”
• 20. Two modular equations
• 21. A letter from Fitzroy House
• 22. The cubic functions of Borwein, Borwein and Garvan
• 23. Some classical results on representations
• 24. Further classical results on representations
• 25. Further results on representations
• 26. Even more representation results
• 27. Representation results and Lambert series
• 28. The Jordan–Kronecker identity
• 29. Melham’s identities
• 30. Partitions into four squares
• 31. Partitions into four distinct squares of equal parity
• 32. Partitions with odd parts distinct
• 33. Partitions with even parts distinct
• 34. Some identities involving phi(q) and  psi(q)
• 35. Some useful parametrisations
• 36. Overpartitions
• 37. Bipartitions with odd parts distinct
• 38. Overcubic partitions
• 39. Generalised Frobenius partitions
• 40. Some modular equations of Ramanujan
• 41. Identities involving k = qR(q)R(q2)2
• 42. Identities involving v=q1/2(q,q7;q8)infinity/(q3,q5;q8)infinity
• 43. Ramanujan's tau function
• Appendix
• Index.