Zeta functions of Ramanujan graphs and modular forms

Abstract

We will investigate the relationship between Ihara's zeta functions of Ramanujan graphs and Hasse-Weil's congruent zeta functions of modular curves. As an application we will describe the limit value of Hasse-Weil's congruent zeta functions in terms of the corresponding Ramanujan graphs. Moreover we will show a congruence relation of the Fourier coefficients of a normalized Hecke eigenform of weight 2.

arXiv admin note: text overlap with arXiv:1905.03417

Cited by in corpus (2)

• A tower of Ramanujan graphs and a reciprocity law of graph zeta functions
• On the space of theta functions for a prime level