Number Theory

Title: Ray class fields of conductor (p)
Speaker: Maria Stadnik
Speaker Info: Northwestern
Brief Description:
Special Note:

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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