The generalized Borwein conjecture. I. The Burge transform

Simple item page
dc.creatorWarnaar, S. Ole
dc.date2000-11-27
dc.date.accessioned2026-07-07T04:38:51Z
dc.date.available2026-07-07T04:38:51Z
dc.descriptionGiven 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\pm 1, but an altogether different sum side, based on the representation of (a/b-1)^{\pm 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.
dc.description25 pages, AMS-LaTeX
dc.identifierhttps://arxiv.org/abs/math/0011220
dc.identifierhttp://arxiv.org/abs/math/0011220
dc.identifierContemp. Math. 291 (2001), 243--267
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60440
dc.subjectCombinatorics
dc.subjectQuantum Algebra
dc.subjectPrimary 05A15, 05A19; Secondary 33D15
dc.titleThe generalized Borwein conjecture. I. The Burge transform
dc.typetext

Files

Collections

arXiv