Zeta functions of Ramanujan graphs and modular forms
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Publication:4566348
zbMATH Open1388.05091arXiv1905.04297MaRDI QIDQ4566348
Publication date: 14 June 2018
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.
Full work available at URL: https://arxiv.org/abs/1905.04297
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Related Items (9)
Deitmar schemes, graphs and zeta functions ⋮ On the zeta functions of supersingular isogeny graphs and modular curves ⋮ Spectral zeta functions of graphs and the Riemann zeta function in the critical strip ⋮ Fourier series of modular graph functions ⋮ Elliptic curves over finite fields and Ramanujan graphs on two vertices ⋮ On ordinary isogeny graphs with level structures ⋮ On towers of isogeny graphs with full level structures ⋮ Absence of irreducible multiple zeta-values in melon modular graph functions ⋮ Modular graph functions and asymptotic expansions of Poincaré series
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