507 research outputs found
Mahler measures and Fuglede--Kadison determinants
The Mahler measure of a function on the real d-torus is its geometric mean
over the torus. It appears in number theory, ergodic theory and other fields.
The Fuglede-Kadison determinant is defined in the context of von Neumann
algebra theory and can be seen as a noncommutative generalization of the Mahler
measure. In the paper we discuss and compare theorems in both fields,
especially approximation theorems by finite dimensional determinants. We also
explain how to view Fuglede-Kadison determinants as continuous functions on the
space of marked groups
Horizontal factorizations of certain Hasse--Weil zeta functions - a remark on a paper by Taniyama
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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