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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.04297
- arXiv:
- arXiv:1905.04297
- Bibcode:
- 2019arXiv190504297S
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- arXiv admin note: text overlap with arXiv:1905.03417