Madeline.Dawsey

Affiliation: University of Texas at Tyler

Title Of Talk: Densities of Subsets of Primes in the Spirit of Alladi

Abstract: Inspired by work of Alladi in the 1970s, a flurry of activity over the last ten years has resulted in new formulas for densities of sets of prime numbers. Most of our understanding of the distribution of primes comes from the Prime Number Theorem. More specifically, one can ask whether the methods from analytic number theory yield formulas for densities of subsets of primes. One famous instance of this is the strong form of Dirichlet’s famous theorem on primes in arithmetic progressions. In 2017, we established formulations of Dirichlet’s Theorem, and more generally the Chebotarev Density Theorem, which may be viewed as the non-abelian extension of Alladi’s work. Following this work, several further generalizations by Sweeting—Wu, Kural—McDonald—Sah, Ono—Schneider—Wagner, and others have led to many new density formulas.

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