Ruelle type L-functions versus determinants of Laplacians for torsion free abelian groups

Nobushige Kurokawa, Masato Wakayama, Yoshinori Yamasaki

Research output: Contribution to journalArticle

Abstract

We study Ruelle's type zeta and L-functions for a torsion free abelian group Γ of rank v < 2 defined via an Euler product. It is shown that the imaginary axis is a natural boundary of this zeta function when v = 2, 4 and 8, and in particular, such a zeta function has no determinant expression. Thus, conversely, expressions like Euler's product for the determinant of the Laplacians of the torus ℝv/Γ defined via zeta regularizations are investigated. Also, the limit behavior of an arithmetic function arising from the Ruelle type zeta function is observed.

Original languageEnglish
Pages (from-to)957-979
Number of pages23
JournalInternational Journal of Mathematics
Volume19
Issue number8
DOIs
Publication statusPublished - Sep 1 2008

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Torsion-free Abelian Group
L-function
Riemann zeta function
Determinant
Euler Product
Arithmetic Functions
Limit Behavior
Regularization
Torus

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Ruelle type L-functions versus determinants of Laplacians for torsion free abelian groups. / Kurokawa, Nobushige; Wakayama, Masato; Yamasaki, Yoshinori.

In: International Journal of Mathematics, Vol. 19, No. 8, 01.09.2008, p. 957-979.

Research output: Contribution to journalArticle

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