On zeta functions of arithmetically defined graphs
Arithmetically defined graphs \(X(n)\), namely quotients of the Bruhat-Tits tree over a local field, are studied, using results from \textit{I. Rust} [Finite Fields Appl. 4, No. 4, 283-306 (1998; Zbl 0933.20033)]. Explicit formulae for the zeta function of \(X(n)\) for small \(n\) are given and, by employing techniques from \textit{K. Hashimoto} [Adv. Stud. Pure Math. 15, 211-280 (1989; Zbl 0709.22005)], new infinite families of Ramanujan graphs are constructed from \(X(n)\).
scientific article; zbMATH DE number 1398791