Ruelle type zeta functions for tori and some arithmetics

Nobushige Kurokawa, Masato Wakayama

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1 Citation (Scopus)

Abstract

We introduce various Ruelle type zeta functions ζL (s) according to a choice of homogeneous "length functions" for a lattice L in ℂ via Euler products. The logarithm of each ζL (s) yields naturally a certain arithmetic function. We study the asymptotic distribution of averages of such arithmetic functions. Asymptotic behavior of the zeta functions at the origin s = 0 are also investigated.

Original languageEnglish
Pages (from-to)691-715
Number of pages25
JournalInternational Journal of Mathematics
Volume15
Issue number7
DOIs
Publication statusPublished - Sep 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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