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RUELLE TYPE ZETA FUNCTIONS FOR TORI AND SOME ARITHMETICS

Authors :
Masato Wakayama
Nobushige Kurokawa
Source :
International Journal of Mathematics. 15:691-715
Publication Year :
2004
Publisher :
World Scientific Pub Co Pte Lt, 2004.

Abstract

We introduce various Ruelle type zeta functions ζL(s) according to a choice of homogeneous "length functions" for a lattice L in [Formula: see text] 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.

Subjects

Subjects :
Discrete mathematics
Pure mathematics
Polylogarithm
General Mathematics
Proof of the Euler product formula for the Riemann zeta function
Riemann zeta function
Ruelle zeta function
Arithmetic zeta function
symbols.namesake
Riemann hypothesis
symbols
Selberg zeta function
Prime zeta function
Mathematics

Details

ISSN :
17936519 and 0129167X
Volume :
15
Database :
OpenAIRE
Journal :
International Journal of Mathematics
Accession number :
edsair.doi...........a22ae04e2b3605d5207e99bf3234ceff
Full Text :
https://doi.org/10.1142/s0129167x0400251x
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