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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convergence of zeta functions of graphs
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by Bryan Clair and Shahriar Mokhtari-Sharghi
Proc. Amer. Math. Soc. 130 (2002), 1881-1886
DOI: https://doi.org/10.1090/S0002-9939-02-06532-2
Published electronically: 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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Bibliographic 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
  • Received by editor(s): August 4, 2000
  • Published electronically: February 27, 2002
  • Communicated by: Dennis A. Hejhal
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 1881-1886
  • MSC (2000): Primary 11M41; Secondary 05C25
  • DOI: https://doi.org/10.1090/S0002-9939-02-06532-2
  • MathSciNet review: 1896018