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

Contenu
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 RogersRamanujan identities and the RogersRamanujan continued fraction.- 16. The series expansion of the RogersRamanujan 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 JordanKronecker 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.