用连分数表示的Pell方程解的双对数恒等式
Dilogarithm identities for solutions to Pell's equation in terms of continued fraction convergents
摘要：
本文给出了双对数函数与Pell方程$x^2-ny^2 = \pm 1$解之间的一种新的联系。对于每一个解决方案$x,y$佩尔方程，我们得到一个双对数的身份，其条款是由相关的单位$x+y\sqrt{n} \in \Z[\sqrt{n}]$的连分数扩展。我们进一步表明，拉马努金的双对数值的身份对应于一个身份的正则理想双曲六边形。
英文摘要：
In this paper we give describe a new connection between the dilogarithm function and solutions to Pell's equation $x^2-ny^2 = \pm 1$. For each solution $x,y$ to Pell's equation we obtain a dilogarithm identity whose terms are given by the continued fraction expansion of the associated unit $x+y\sqrt{n} \in \Z[\sqrt{n}]$. We further show that Ramanujan's dilogarithm value-identities correspond to an identity for the regular ideal hyperbolic hexagon.
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