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arXiv · 1105.3938

The Discriminant of an Algebraic Torus

R. A. Bitan
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Abstract

For a torus T defined over a global field K, we revisit an analytic class number formula obtained by Shyr in the 1970's as a generalization of Dirichlet's class number formula. We prove a local-global presentation of the quasi-discriminant of T, which enters into this formula, in terms of cocharacters of T. This presentation can serve as a more natural definition of this invariant.

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R. A. Bitan. 2011-05-19. The Discriminant of an Algebraic Torus. https://doi.org/10.1016/j.jnt.2011.03.001

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