Number Theory Seminar
Date: December 3, 2018
Time: 11:00AM - 12:00PM
Location: BLOC 220
Speaker: Madeline Locus Dawsey, Emory University
Title: Densities of subsets of prime numbers
Abstract: Thanks to the Prime Number Theorem, a lot is known about the distribution of prime numbers. In particular, one can ask whether the methods from analytic number theory yield formulas for densities of subsets of prime numbers. One famous instance of this is the strong form of Dirichlet's famous theorem on primes in arithmetic progressions. Here, we give new formulations of Dirichlet's Theorem, and more generally the Chebotarev Density Theorem, by offering completely new formulas expressing densities of suitable subsets of prime numbers. Our work can be thought of as the non-abelian extension of a theorem of Alladi from the 1970s.
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