4:00 pm Thursday, April 10, 2014

Arul Shankar (Harvard)

I will discuss a classical result of Davenport, establishing asymptotics for the number of $Gl_2(Z)$-orbits on integral binary cubic forms having bounded discriminant, with a power saving error term. I will then discuss an averaging method of Bhargava's that improves Davenport's power saving error term to an optimal one. Finally, we introduce a refinement that allows us to determine the second main term for this count! The final refinement is joint work with Bhargava and Tsimerman.