The Riemann hypothesis for period polynomials of Hilbert modular forms

There have been a number of recent works on the theory period polynomials and their zeros. In particular, zeros shown to satisfy “Riemann Hypothesis” in both classical settings for cohomological versions extending setting case higher derivatives L-functions. thus appears be general phenomenon behind these phenomena. this paper, we explore further generalizations by defining natural analogue Hilbert modular forms. We then prove that similar Riemann Hypotheses hold situation as well.