On zeta functions of arithmetically defined graphs (Q1964069)
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scientific article; zbMATH DE number 1398791
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On zeta functions of arithmetically defined graphs |
scientific article; zbMATH DE number 1398791 |
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On zeta functions of arithmetically defined graphs (English)
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19 March 2000
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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 \(X(n)\).
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Bruhat-Tits tree
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L-function
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zeta function
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Ramanujan graph
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0.93842274
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0.93333924
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