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Ihara Zeta Functions for Periodic Simple Graphs

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Book cover C*-algebras and Elliptic Theory II

Part of the book series: Trends in Mathematics ((TM))

Abstract

The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment developed by Stark and Terras for finite graphs.

The first and second authors were partially supported by MIUR, GNAMPA and by the European Network “Quantum Spaces — Noncommutative Geometry” HPRN-CT-2002-00280. The third author was partially supported by the National Science Foundation, the Academic Senate of the University of California, and GNAMPA.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, I-00133, Roma, Italy

    Daniele Guido & Tommaso Isola

  2. Department of Mathematics, University of California, Riverside, CA, 92521-0135, USA

    Michel L. Lapidus

Authors
  1. Daniele Guido
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  2. Tommaso Isola
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  3. Michel L. Lapidus
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210, USA

    Dan Burghelea

  2. Department of Mathematics, Massachusetts Institute of Technology, Room 2-174 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Richard Melrose

  3. Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119992, Moscow, Russia

    Alexander S. Mishchenko  & Evgenij V. Troitsky  & 

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Guido, D., Isola, T., Lapidus, M.L. (2008). Ihara Zeta Functions for Periodic Simple Graphs. In: Burghelea, D., Melrose, R., Mishchenko, A.S., Troitsky, E.V. (eds) C*-algebras and Elliptic Theory II. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8604-7_5

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