Zeta functions of Ramanujan graphs and modular forms

2019/05/10 by Kennichi Sugiyama, Sugiyama, Kennichi · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1905.04297

openalex publication_date 2019/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

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

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