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

Nobushige Kurokawa, Masato Wakayama, Yoshinori Yamasaki

研究成果: Contribution to journalArticle査読

抄録

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.

本文言語英語
ページ(範囲)957-979
ページ数23
ジャーナルInternational Journal of Mathematics
19
8
DOI
出版ステータス出版済み - 9 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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