## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** Ray class fields of conductor (p)

**Speaker:** Maria Stadnik

**Speaker Info:** Northwestern

**Brief Description:**

**Special Note**:

**Abstract:**

Let K be Galois extension of the rational numbers, let H be the
Hilbert class field of K, and let zeta denote a primitive p-th root of
unity. We conjecture that under certain conditions on K, there are
infinitely many p completely split in K for which the ray class field of
conductor (p) = pO_K equals H(zeta + zeta^{-1}). We give motivation for
why a conjectural density should exist and explain how to reformulate this
question into a set of simpler questions about certain modules over
Gal(K/Q). From there we can adapt methods from Hooley's proof of Artin's
conjecture on primitive roots (which assumes the generalized Riemann
hypothesis) to help solve the problem. We give results for multiquadratic
fields assuming the GRH.

**Date:** Monday, May 10, 2010

**Time:** 3:00PM

**Where:** Lunt 107

**Contact Person:** Florian Herzig

**Contact email:** herzig@math

**Contact Phone:** 847-467-1898

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