The generalized Borwein conjecture. I. The Burge transform
作者： S. Ole Warnaar
DOI:
关键词: Conjecture 、 Identity (mathematics) 、 Combinatorics 、 Mathematics 、 Coprime integers 、 Ordered pair 、 Binary tree 、 Discrete mathematics 、 Product (mathematics) 、 Tree (set theory) 、 Type (model theory)
摘要: Given an arbitrary ordered pair of coprime integers (a,b) we obtain a identities the Rogers--Ramanujan type. These have same product side as (first) Andrews--Gordon identity for modulus 2ab\pm 1, but altogether different sum side, based on representation (a/b-1)^{\pm 1} continued fraction. Our proof, which relies Burge transform, first establishes binary tree polynomial identities. Each in this settles special case Bressoud's generalized Borwein conjecture.
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harvard.edu参考文章(20)
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