English

Horizontal factorizations of certain Hasse--Weil zeta functions - a remark on a paper by Taniyama

Algebraic Geometry 2012-02-16 v1 Number Theory

Abstract

In one of his papers, using arguments about l-adic representations, Taniyama expresses the zeta function of an abelian variety over a number field as an infinite product of modified Artin L-functions. The latter can be further decomposed as products of modified Dedekind zeta functions. After recalling Taniyama's work, we give a simple geometric proof of the resulting product formula for abelian and more general group schemes.

Keywords

Cite

@article{arxiv.1202.3274,
  title  = {Horizontal factorizations of certain Hasse--Weil zeta functions - a remark on a paper by Taniyama},
  author = {Christopher Deninger and Dimitri Wegner},
  journal= {arXiv preprint arXiv:1202.3274},
  year   = {2012}
}