AI 中文总结
本文证明Lewis与Zagier构造的某类函数中的首个例子是Hecke本征形式，并据此确定Hecke算子对高阶Herglotz-Zagier函数导数的作用，导出相关多项函数方程。
AI 中文摘要
在一篇开创性论文中，Lewis和Zagier构造了多种满足三项函数方程的函数。本文研究其中首个例子，证明该函数是关于Hecke算子的Hecke本征形式，这些算子作用于周期上。随后利用该结果确定上述算子对高阶Herglotz-Zagier函数导数的作用，该作用导出了该函数满足的一族多项函数方程。
英文摘要
In a seminal paper, Lewis and Zagier constructed variety of functions satisfying the three-term functional equations. In this article, we consider the first example among them and establish that the function is a Hecke eigen form with respect to the Hecke operators, which acts on periods. We then utilize this result to determine the action of the aforementioned operators on the derivative of the Higher order Herglotz-Zagier function. The action leads to a family of multi-term functional equations satisfied by the function.
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