Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-27T18:38:22.418Z Has data issue: false hasContentIssue false
  • English
  • Français

Combinatorial L2-determinants

Published online by Cambridge University Press:  20 January 2009

Anton Deitmar
Anton Deitmar
Affiliation:
Mathematics Institute, INF 288, 69120 Heidelberg, Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that the zeta function of a regular graph admits a representation as a quotient of a determinant over a L2-determinant of the combinatorial Laplacian.

Keywords

zeta functionsgraphsL2-theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 1 , February 2000 , pp. 185 - 194
Copyright
Copyright © Edinburgh Mathematical Society 2000

References

1.Bass, H., The Ihara–Selberg zeta function of a tree lattice, Int. J. Math. 3 (1992), 717–797.CrossRefGoogle Scholar
2.Deitmar, A., A determinant formula for the generalized Selberg zeta function, Q. J. Math. 47 (1996), 435–453.CrossRefGoogle Scholar
3.Deitmar, A., Regularized and L 2-determinants, Proc. Lond. Math. Soc. 76 (1998), 150–174.CrossRefGoogle Scholar
4.Deitmar, A., Geometric zeta functions on p-adic groups, Math. Japon. 47 (1998), 1–17.Google Scholar
5.Hashimoto, K., Zeta functions of finite graphs and representations of p-adic groups. Automorphic forms and geometry of arithmetic varieties, Adv. Stud. Pure Math. 15 (1989), 211–280.CrossRefGoogle Scholar
6.Lück, W., Approximating L 2-invariants by their finite-dimensional analogues, Geom. Funct. Analysis 4 (1994), 455–481.CrossRefGoogle Scholar