A Bailey lattice
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- by Jeremy Lovejoy PDF
- Proc. Amer. Math. Soc. 132 (2004), 1507-1516 Request permission
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
- A. K. Agarwal, G. E. Andrews, and D. M. Bressoud, The Bailey lattice, J. Indian Math. Soc. (N.S.) 51 (1987), 57–73 (1988). MR 988309
- George E. Andrews, Connection coefficient problems and partitions, Relations between combinatorics and other parts of mathematics (Proc. Sympos. Pure Math., Ohio State Univ., Columbus, Ohio, 1978) Proc. Sympos. Pure Math., XXXIV, Amer. Math. Soc., Providence, R.I., 1979, pp. 1–24. MR 525316
- George E. Andrews, Ramanujan’s “lost” notebook. I. Partial $\theta$-functions, Adv. in Math. 41 (1981), no. 2, 137–172. MR 625891, DOI 10.1016/0001-8708(81)90013-X
- George E. Andrews, $q$-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra, CBMS Regional Conference Series in Mathematics, vol. 66, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986. MR 858826
- George E. Andrews, Multiple series Rogers-Ramanujan type identities, Pacific J. Math. 114 (1984), no. 2, 267–283. MR 757501
- George E. Andrews, Bailey chains and generalized Lambert series. I. Four identities of Ramanujan, Illinois J. Math. 36 (1992), no. 2, 251–274. MR 1156626
- George E. Andrews, Freeman J. Dyson, and Dean Hickerson, Partitions and indefinite quadratic forms, Invent. Math. 91 (1988), no. 3, 391–407. MR 928489, DOI 10.1007/BF01388778
- George E. Andrews and Dean Hickerson, Ramanujan’s “lost” notebook. VII. The sixth order mock theta functions, Adv. Math. 89 (1991), no. 1, 60–105. MR 1123099, DOI 10.1016/0001-8708(91)90083-J
- D. M. Bressoud, The Bailey lattice: an introduction, Ramanujan revisited (Urbana-Champaign, Ill., 1987) Academic Press, Boston, MA, 1988, pp. 57–67. MR 938960
- F. Franklin, Sur le développement du produit infini $(1-x)(1-x^2) (1-x^3)...$, Comptes Rendus 82 (1881), 448-450.
- George Gasper and Mizan Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990. With a foreword by Richard Askey. MR 1052153
- Jeremy Lovejoy, Lacunary partition functions, Math. Res. Lett. 9 (2002), no. 2-3, 191–198. MR 1909637, DOI 10.4310/MRL.2002.v9.n2.a5
- Anne Schilling and S. Ole Warnaar, A higher level Bailey lemma: proof and application, Ramanujan J. 2 (1998), no. 3, 327–349. MR 1651423, DOI 10.1023/A:1009746932284
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- S. Ole Warnaar, 50 years of Bailey’s lemma, Algebraic combinatorics and applications (Gößweinstein, 1999) Springer, Berlin, 2001, pp. 333–347. MR 1851961
- S. O. Warnaar, Partial theta functions I: beyond the lost notebook, preprint.
Additional Information
- Jeremy Lovejoy
- Affiliation: CNRS, LaBRI, Université Bordeaux I, 351 Cours de la libération, 33405 Talence Cedex, France
- MR Author ID: 671259
- Email: lovejoy@labri.fr
- Received by editor(s): January 23, 2003
- Published electronically: October 24, 2003
- Communicated by: Wen-Ching Winnie Li
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1507-1516
- MSC (2000): Primary 33D15
- DOI: https://doi.org/10.1090/S0002-9939-03-07247-2
- MathSciNet review: 2053359