Supercharacters and the Chebotarev density theorem
Volume 185 / 2018
Acta Arithmetica 185 (2018), 281-295
MSC: 11M26, 11N45, 20C15.
DOI: 10.4064/aa180320-22-6
Published online: 10 August 2018
Abstract
We employ the theory of supercharacters introduced by Diaconis and Isaacs to refine the previous work of M. R. Murty, V. K. Murty, and Saradha by deriving effective versions of the Chebotarev density theorem for certain unions of conjugacy classes without using Artin’s conjecture. As an application, we remove the assumption of Artin’s conjecture from a result of Akbary and Ghioca on the Titchmarsh divisor problem for elliptic curves.
