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Convergence of zeta functions of graphs

Author(s): Bryan Clair; Shahriar Mokhtari-Sharghi
Journal: Proc. Amer. Math. Soc. 130 (2002), 1881-1886.
MSC (2000): Primary 11M41; Secondary 05C25
Posted: February 27, 2002
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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: 10.1090/S0002-9939-02-06532-2
PII: S 0002-9939(02)06532-2
Received by editor(s): August 4, 2000
Posted: February 27, 2002
Communicated by: Dennis A. Hejhal
Copyright of article: Copyright 2002, American Mathematical Society

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