16-rank of class groups of quadratic number fields

16-rank of class groups of quadratic number fields

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Djordjo Milovic , IAS
Fine Hall 214

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.