DATE: Tuesday, December 8 (2009), at 10:40am
PLACE: LIT 305
SPEAKER: Frank Patane
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TITLE:
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The Number of Genera for Binary Quadratic Forms
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ABSTRACT:
We begin with a simple proof showing that at most half
the number of all possible genera exist. We then count ambiguous
forms of a fixed discriminant, and connect this to the number of
possible genera. Combined with the fact that every form in the
principal genus is a square, we will have the conclusion that
exactly half all possible genera exist. Lastly we see exactly
which characters exist for fundamental discriminants.
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