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.