16-rank of class groups of quadratic number fields

Joint IAS/Princeton University Number Theory Seminar
Topic:16-rank of class groups of quadratic number fields
Speaker:Djordjo Milovic
Affiliation:Member, School of Mathematics
Date:Thursday, February 16
Time/Room:4:30pm - 5:30pm/Fine 214, Princeton University

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 a density result for the 16-rank in the family of quadratic number fields of discriminant $-8p$ with $p$ a prime. We will also explain certain limitations of the method arising from reliance on short character sum estimates.