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The Power of q

A Personal Journey
BuchGebunden
415 Seiten
Englisch
Springererschienen am16.08.20171st ed. 2017
The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities.mehr
Verfügbare Formate
BuchGebunden
EUR139,09
BuchKartoniert, Paperback
EUR139,09
E-BookPDF1 - PDF WatermarkE-Book
EUR128,39

Produkt

KlappentextThe book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities.
Zusammenfassung
Aptly conveys the beauty and power of q-series

Accessible to advanced undergraduates, graduate students, and researchers

Historical notes enrich the readers understanding of the subject

First monograph to focus uniquely on q-series

Includes supplementary material: sn.pub/extras

Includes supplementary material: sn.pub/extras
Details
ISBN/GTIN978-3-319-57761-6
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2017
Erscheinungsdatum16.08.2017
Auflage1st ed. 2017
ReiheDevelopments in Mathematics
Seiten415 Seiten
SpracheEnglisch
Gewicht818 g
IllustrationenXXIV, 415 p.
Artikel-Nr.42730446

Inhalt/Kritik

Inhaltsverzeichnis
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) â¡ 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. Somemodular 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.mehr