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Convergence of zeta functions of graphs


Authors: Bryan Clair and Shahriar Mokhtari-Sharghi
Journal: Proc. Amer. Math. Soc. 130 (2002), 1881-1886
MSC (2000): Primary 11M41; Secondary 05C25
Published electronically: February 27, 2002
MathSciNet review: 1896018
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Abstract: The $L^{2}$-zeta function of an infinite graph $Y$ (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by $Y$, the normalized zeta functions of the finite graphs converge to the $L^{2}$-zeta function of $Y$.


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Additional Information

Bryan Clair
Affiliation: Department of Mathematics, Saint Louis University, 220 N. Grand Ave., St. Louis, Missouri 63103
Email: bryan@slu.edu

Shahriar Mokhtari-Sharghi
Affiliation: Department of Mathematics, Long Island University, Brooklyn Campus, 1 University Plaza, Brooklyn, New York 11201
Email: mokhtari@liu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06532-2
Received by editor(s): August 4, 2000
Published electronically: February 27, 2002
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2002 American Mathematical Society