English

Zeta functions of Ramanujan graphs and modular forms

Algebraic Geometry 2019-05-14 v1

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.

Keywords

Cite

@article{arxiv.1905.04297,
  title  = {Zeta functions of Ramanujan graphs and modular forms},
  author = {Kennichi Sugiyama},
  journal= {arXiv preprint arXiv:1905.04297},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1905.03417

R2 v1 2026-06-23T09:03:10.455Z