Editing Ihara zeta function (section)

In [[mathematics]], the '''Ihara zeta function''' is a [[zeta function]] associated with a finite [[Graph (discrete mathematics)|graph]]. It closely resembles the [[Selberg zeta function]], and is used to relate closed walks to the [[Spectrum of a matrix|spectrum]] of the [[adjacency matrix]]. The Ihara zeta function was first defined by [[Yasutaka Ihara]] in the 1960s in the context of [[discrete group|discrete subgroups]] of the two-by-two [[p-adic number|p-adic]] [[special linear group]]. [[Jean-Pierre Serre]] suggested in his book ''Trees'' that Ihara's original definition can be reinterpreted graph-theoretically. It was [[Toshikazu Sunada]] who put this suggestion into practice in 1985. As observed by Sunada, a [[regular graph]] is a [[Ramanujan graph]] if and only if its Ihara zeta function satisfies an analogue of the [[Riemann hypothesis]].<ref>Terras (1999) p.&nbsp;678</ref>