Ihara Zeta Functions of Infinite Weighted Graphs

Anton Deitmar

Type: Article

Publication Date: 2015-01-01

Citations: 9

DOI: https://doi.org/10.1137/140957925

Abstract

The theory of Ihara zeta functions is extended to infinite graphs which are weighted and of finite total weight. In this case one gets meromorphic instead of rational functions and the classical determinant formulas of Bass and Ihara hold true with Fredholm determinants.

Locations

SIAM Journal on Discrete Mathematics - View
arXiv (Cornell University) - View - PDF

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+	The Ihara zeta function for infinite graphs	2018	Daniel Lenz Felix Pogorzelski Marcel Schmidt
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+ PDF Chat	Heat kernels on regular graphs and generalized Ihara zeta function formulas	2014	Gautam Chinta Jay Jorgenson Anders Karlsson
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Works Cited by This (12)

Action	Title	Year	Authors
+	ARTIN TYPE L-FUNCTIONS AND THE DENSITY THEOREM FOR PRIME CYCLES ON FINITE GRAPHS	1992	Ki-ichiro Hashimoto
+	Zeta functions of graphs with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="double-struck">Z</mml:mi></mml:math> actions	2008	Bryan Clair
+	Lattices in rank one Lie groups over local fields	1991	Alexander Lubotzky
+ PDF Chat	Ihara's zeta function for periodic graphs and its approximation in the amenable case	2008	Daniele Guido Tommaso Isola Michel L. Lapidus
+	The non-backtracking spectrum of the universal cover of a graph	2014	Omer Angel Joel Friedman Shlomo Hoory
+	Zeta Functions of Discrete Groups Acting on Trees	2001	Bryan Clair Shahriar Mokhtari-Sharghi
+ PDF Chat	On discrete subgroups of the two by two projective linear group over $\mathfrak{p}$ -adic fields	1966	Yasutaka Ihara
+ PDF Chat	Zeta functions of finite graphs and coverings, III	2006	Audrey Terras H. Stärk
+	On Zeta Functions of Arithmetically Defined Graphs	1999	Ortwin Scheja
+	THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE	1992	Hyman Bass