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arXiv · 1905.03417

A tower of Ramanujan graphs and a reciprocity law of graph zeta functions

Kennichi Sugiyama
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Abstract

Let l be an odd prime. We will construct a tower of connected regular Ramanujan graph of degree l+1 from of modular curves. This supplies an example of a collection of graphs whose discrete Cheeger constants are bounded by (sqrt{l}-1)^{2}/2 from below. We also show graph (or Ihara) zeta functions satisfy a certain reciprocity law.

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Kennichi Sugiyama. 2019-05-09. A tower of Ramanujan graphs and a reciprocity law of graph zeta functions. https://arxiv.org/abs/1905.03417

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