Talk:Dirichlet's unit theorem

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Would be nice to add some more explicitly geometric description of the regulator as the volume of the quotient of trace-zero space by the lattice of units, e.g. like in Neukirch's Algebraic Number Theory p43. Dmharvey 02:08, 16 July 2006 (UTC)
 * Wow and I can't seem to find an article on the elliptic regulator anywhere... is this really possible? Dmharvey 02:11, 16 July 2006 (UTC)

Could anyone please expand/elaborate on the sentence "The map taking a unit u to the vector with entries Nilog|ui| has image in the r-dimensional subspace of Rr+1 consisting of all vectors whose entries have sum 0, and by Dirichlet's unit theorem the image is a lattice in this subspace." I don't see how this follows from the unit theorem. — Preceding unsigned comment added by Octonion (talk • contribs) 23:00, 23 March 2012 (UTC)

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