2000/11/27 by S. Ole Warnaar · 1 citation
Mathematics · #math.CO #math.QA #msc:05A15 #msc:05A19 #msc:33D15
published as Contemp. Math. 291 (2001), 243--267 · 25 pages, AMS-LaTeX
arxiv created 2000/11/27 · arxiv updated 2009/11/30
Given an arbitrary ordered pair of coprime integers (a,b) we obtain a pair of identities of the Rogers--Ramanujan type. These identities have the same product side as the (first) Andrews--Gordon identity for modulus 2ab± 1, but an altogether different sum side, based on the representation of (a/b-1)± 1 as a continued fraction. Our proof, which relies on the Burge transform, first establishes a binary tree of polynomial identities. Each identity in this Burge tree settles a special case of Bressoud's generalized Borwein conjecture.