论文标题
希尔伯特模块化的时期多项式的Riemann假设
The Riemann Hypothesis for period polynomials of Hilbert modular forms
论文作者
论文摘要
关于时期多项式及其零的理论，最近有许多著作。特别是，已显示多项式的零可以满足经典设置和共同体版本的“ Riemann假设”，以将经典设置扩展到$ L $函数的较高衍生物的情况下。因此，这些现象背后似乎有一个普遍的现象。在本文中，我们通过定义希尔伯特模块化形式的自然类似物来探讨进一步的概括。然后，我们证明在这种情况下，类似的Riemann假设也存在。
There have been a number of recent works on the theory of period polynomials and their zeros. In particular, zeros of period polynomials have been shown to satisfy a "Riemann Hypothesis" in both classical settings and for cohomological versions extending the classical setting to the case of higher derivatives of $L$-functions. There thus appears to be a general phenomenon behind these phenomena. In this paper, we explore further generalizations by defining a natural analogue for Hilbert modular forms. We then prove that similar Riemann Hypotheses hold in this situation as well.
