Jonathan Hanke

Affiliation: University of Georgia

Email: jonhanke@gmail.com

Title Of Talk: Class numbers and Mass formulas for quadratic forms

Abstract: This talk will describe how to use exact mass formulas to determine quadratic forms of small class number, particularly those positive definite forms of class number one. The mass of a quadratic form connects the class number (i.e. number of classes in the genus) of a quadratic form with the volume of its adelic stabilizer, and is explicitly computable in terms of special values of zeta functions and their twists. Comparing this with known results about the sizes of automorphism groups one can make precise statements about the growth of the class number, and in principle determine those quadratic forms of small class number. These ideas can also be expressed more generally in the context of a linear algebraic group, and similar results should hold in that context as well.

Last update made Sat May 16 10:58:39 EDT 2009.
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