http://math.fontein.de Focussed on, but not limited to Computational Number Theory Sat, 30 Jul 2011 12:35:49 +0000 en hourly 1 http://wordpress.org/?v=3.1 http://math.fontein.de/2010/07/27/rigorous-arithmetic-in-the-arakelov-divisor-class-group-of-a-number-field/ http://math.fontein.de/2010/07/27/rigorous-arithmetic-in-the-arakelov-divisor-class-group-of-a-number-field/#comments Tue, 27 Jul 2010 09:50:37 +0000 Felix Fontein http://math.fontein.de/?p=778 This year at the IX. Algorithmic Number Theory Symphosium, held in Nancy, I had a poster in the poster session. You can see it here (click to see a larger version):

You can also get a PDF version here (9.1 MB).
The poster discusses how to effectively compute in the Arakelov divisor class group of a number field , which is assumed to be totally real in the current implementation described in the poster, but the same method works as long as there is at least one real embedding of . In case is totally imaginary, the only thing which gets more complicated is doing comparisms. The arithmetic uses -representations as the main tool, i.e. it allows to compute in the infrastructure of .

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