广义Borwein猜想I. Burge变换
The generalized Borwein conjecture. I. The Burge transform
摘要：
给定互质整数（a，b）的任意序偶对，我们得到一对Rogers-Ramanujan型恒等式.这些恒等式与模2ab \pm 1的（第一个）安德鲁斯-戈登恒等式具有相同的乘积侧，但是基于（a/b-1）^{ \pm 1}作为连分数的表示，它们具有完全不同的和侧。我们的证明，这依赖于伯奇变换，首先建立一个二叉树的多项式身份。在这个Burge树中的每个身份解决了Bressoud的广义Borwein猜想的一个特殊情况。
英文摘要：
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\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.
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