Using Mass formulas to Enumerate Definite Quadratic Forms of Bounded Class Number

Algebra Seminar
Tuesday, January 24, 2012 - 14:05
1 hour (actually 50 minutes)
Skiles 006
University of Georgia
This talk will describe some recent results using exact massformulas to determine all definite quadratic forms of small class number inn>=3 variables, particularly those of class number one.The mass of a quadratic form connects the class number (i.e. number ofclasses in the genus) of a quadratic form with the volume of its adelicstabilizer, and is explicitly computable in terms of special values of zetafunctions.  Comparing this with known results about the sizes ofautomorphism groups, one can make precise statements about the growth ofthe class number, and in principle determine those quadratic forms of smallclass number.We will describe some known results about masses and class numbers (overnumber fields), then present some new computational work over the rationalnumbers, and perhaps over some totally real number fields.