The Riemann Hypothesis for period polynomials of Hilbert modular forms

2020/05/21 by Babei, Angelica, Rolen, Larry, Wagner, Ian
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.10763

Abstract

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.

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