收敛于Gauss-Kuzmin-Wirsing算子特征值的级数的递归构造
Recursive construction of a series converging to the eigenvalues of the Gauss-Kuzmin-Wirsing operator
摘要：
基于作者以前发展的技巧，我们提出了一个猜想：Gauss-Kuzmin-Wirsing算子的第n大（绝对值）特征值的倒数等于某个无穷级数的和.这个系列是循环构建的。它由两个变量X，Y的整数系数的有理函数组成，专门用于X=n和Y=2^n。这就有力地证明了Mayer和Roepstorff关于特征值具有交替符号的猜想。此外，一个非常类似的递归产生一个系列的主导特征值的迈耶-吕尔算子。
英文摘要：
Based on the technique previously developed by the author, we present a conjecture which claims that the reciprocal of the n-th largest (in absolute value) eigenvalue of the Gauss-Kuzmin-Wirsing operator is equal to the sum of a certain infinite series. This series is constructed recurrently. It consists of rational functions with integer coefficients in two variables X, Y, specialized at X=n and Y=2^n. This gives a strong evidence to the conjecture of Mayer and Roepstorff that eigenvalues have alternating sign. Further, a very similar recursion yields a series for the dominant eigenvalue of the Mayer-Ruelle operator.
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