The Riemann hypothesis for period polynomials of Hilbert modular forms

JOURNAL OF NUMBER THEORY

卷:218

Article

Babei, Angelica¹  Rolen, Larry²  Wagner, Ian² 

[1] Univ Montreal, Montreal, PQ, Canada

[2] Vanderbilt Univ, 221 Kirkland Hall, Nashville, TN 37235 USA

关键词: Period polynomials;    Hilbert modular forms;    L-values;    Unimodular polynomials;   

DOI  :  10.1016/j.jnt.2020.07.004

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free