DATE: Tuesday, November 24 (2009), at 10:40am
PLACE: LIT 305
SPEAKER: Frank Patane
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TITLE:
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Genus theory according to Gauss (Part 3)
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ABSTRACT:
In the previous discussion we used the number of ambiguous forms
to help yield a necessary and sufficient condition for a binary
quadratic form to be a square. This week we will get a more
concrete handle on what an ambiguous form looks like, and will use
them to find the number of genera for any discriminant.
We will then consider exactly how to take a "squareroot" of a
form in the principal genus, and look at some examples to illustrate
this squareroot method and to get a firm grasp on the genus theory thus far
considered.
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