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

Christopher Deninger; Dimitri Wegner

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arXiv · 1202.3274

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

Christopher Deninger·Dimitri Wegner

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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.

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Christopher Deninger, Dimitri Wegner. 2012-02-15. Horizontal factorizations of certain Hasse--Weil zeta functions - a remark on a paper by Taniyama. https://arxiv.org/abs/1202.3274

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