Ruelle type zeta functions for tori and some arithmetics

Nobushige Kurokawa; Masato Wakayama

doi:10.1142/S0129167X0400251X

Ruelle type zeta functions for tori and some arithmetics

Nobushige Kurokawa, Masato Wakayama

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Abstract

We introduce various Ruelle type zeta functions ζ_L (s) according to a choice of homogeneous "length functions" for a lattice L in ℂ via Euler products. The logarithm of each ζ_L (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 language	English
Pages (from-to)	691-715
Number of pages	25
Journal	International Journal of Mathematics
Volume	15
Issue number	7
DOIs	https://doi.org/10.1142/S0129167X0400251X
Publication status	Published - Sept 2004

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1142/S0129167X0400251X

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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.",

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AB - 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.

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ER -

Ruelle type zeta functions for tori and some arithmetics

Abstract

All Science Journal Classification (ASJC) codes

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