On a counting problem in number theory

10/02/2012 - 12:15pm
10/02/2012 - 1:10pm
Lenny Fukshansky (CMC)

A classical problem in Diophantine approximation asks for an estimate on the number of points of a given lattice L inside of a fixed compact set S in R^n. While in general very difficult, this problem becomes more tractable under additional assumptions on S. We will briefly review some of the known results in this direction, and will then discuss how such estimates can be used to count the number of points of bounded height over number fields. We will conclude with some related estimates over positive definite quaternion algebras.

Millikan 208 (Pomona College)