English

The Taylor expansion of Ruelle L-function at the origin and the Borel regulator

Differential Geometry 2008-04-18 v1 Number Theory

Abstract

We will prove that Ruelle L-function for a cuspidal local system on an odd dimensional hyperbolic manifold with finite volume satisfies a functional equation and an analog of the Riemann hypothesis. We will also compute its Laurent expansion at the origin and will prove that the second coefficient coincides with a rational multiple of the volume up to a certain contribution from cusps. Moreover if the dimension is three we will identify the leading coefficient. Both of them will be intepreted by the Borel regulator in algebraic K-theory. Also a relation with the L^2-torsion will be discussed.

Keywords

Cite

@article{arxiv.0804.2715,
  title  = {The Taylor expansion of Ruelle L-function at the origin and the Borel regulator},
  author = {Ken-ichi Sugiyama},
  journal= {arXiv preprint arXiv:0804.2715},
  year   = {2008}
}

Comments

50 pages, 0 figures