Signed fundamental domains for totally real number fields
Francisco Diaz y Diaz, Eduardo Friedman

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Abstract
We give a signed fundamental domain for the action on of the totally positive units of a totally real number field of degree . The domain is signed since the net number of its intersections with any -orbit is 1, i. e. for any , Here is the characteristic function of , is a natural orientation of the -dimensional -rational cone , and the inner sum is actually finite. Signed fundamental domains are as useful as Shintani's true ones for the purpose of calculating abelian -functions. They have the advantage of being easily constructed from any set of fundamental units, whereas in practice there is…
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