Joint IAS/Princeton University Number Theory Seminar

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.