Wednesday, April 5, 2017 - 2:30pm
Institute for Advanced Study
We will discuss how Vinogradov's method applies to the study of the 2-part of class groups in certain thin families of quadratic number fields. We will show how the method yields density results for the 16-rank in the families of quadratic number fields parametrized by discriminants of the form -4p and -8p, with p prime. We will also explain certain limitations of the method arising from reliance on short character sum estimates.