Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A Bailey lattice

Author: Jeremy Lovejoy
Journal: Proc. Amer. Math. Soc. 132 (2004), 1507-1516
MSC (2000): Primary 33D15
Published electronically: October 24, 2003
MathSciNet review: 2053359
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We exhibit a technique for generating new Bailey pairs which leads to deformations of classical $q$-series identities, multiple series identities of the Rogers-Ramanujan type, identities involving partial theta functions, and a variety of representations for $q$-series by number-theoretic objects such as weight 3/2 modular forms, ternary quadratic forms, and weighted binary quadratic forms.

References [Enhancements On Off] (What's this?)

  • 1. A. Agarwal, G. E. Andrews, and D. Bressoud, The Bailey Lattice, J. Indian Math. Soc. 51 (1987), 57-73. MR 90i:11113
  • 2. G. E. Andrews, Connection coefficient problems and partitions, Proc. Sympos. Pure Math. 34 (1979), 1-24. MR 80c:33004
  • 3. G. E. Andrews, Ramanujan's ``lost'' notebook I. Partial theta functions, Adv. Math. 41 (1981), 137-172. MR 83m:10034a
  • 4. G. E. Andrews, $q$-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra, CBMS Regional Conference Series in Mathematics 66, American Mathematical Society, Providence, RI, 1986. MR 88b:11063
  • 5. G. E. Andrews, Multiple series Rogers-Ramanujan type identities, Pacific J. Math 114 (1984), 267-283. MR 86c:11084
  • 6. G. E. Andrews, Bailey chains and generalized Lambert series I: Four identities of Ramanujan, Illinois J. Math. 36 (1992), 251-274. MR 93i:11020
  • 7. G. E. Andrews, F. J. Dyson, and D. Hickerson, Partitions and indefinite quadratic forms, Invent. Math. 91 (1988), 391-407. MR 89f:11071
  • 8. G. E. Andrews and D. Hickerson, Ramanujan's ``Lost'' notebook VII: The sixth order mock theta functions, Adv. Math. 89 (1991), 60-105. MR 92i:11027
  • 9. D. M. Bressoud, The Bailey lattice: An introduction, in Ramanujan Revisited, pp. 57-67, Academic Press, Boston, MA, 1988. MR 89f:05018
  • 10. F. Franklin, Sur le développement du produit infini $(1-x)(1-x^2) (1-x^3)...$, Comptes Rendus 82 (1881), 448-450.
  • 11. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990. MR 91d:33034
  • 12. J. Lovejoy, Lacunary partition functions, Math. Res. Lett. 9 (2002), 191-198. MR 2003f:11157
  • 13. A. Schilling and S. O. Warnaar, A higher level Bailey lemma: proof and application, Ramanujan J. 2 (1998), 327-349. MR 99k:11028
  • 14. L. J. Slater, A new proof of Rogers's transformations of infinite series, Proc. London Math. Soc. (2) 53 (1951), 460-475. MR 13:227g
  • 15. S. O. Warnaar, 50 years of Bailey's lemma, Algebraic Combinatorics and Applications, Springer-Verlag, Berlin, 2001, pp. 333-347. MR 2002g:33020
  • 16. S. O. Warnaar, Partial theta functions I: beyond the lost notebook, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 33D15

Retrieve articles in all journals with MSC (2000): 33D15

Additional Information

Jeremy Lovejoy
Affiliation: CNRS, LaBRI, Université Bordeaux I, 351 Cours de la libération, 33405 Talence Cedex, France

Received by editor(s): January 23, 2003
Published electronically: October 24, 2003
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society