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arXiv · 1905.04297

Zeta functions of Ramanujan graphs and modular forms

Kennichi Sugiyama
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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.

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Kennichi Sugiyama. 2019-05-10. Zeta functions of Ramanujan graphs and modular forms. https://arxiv.org/abs/1905.04297

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