On theorems of Barban-Davenport-Halberstam type
by
C. Hooley
University of Wales, Cardiff

In the 1960s Barban on the one hand and Davenport and Halberstam on the other proved a theorem - now often called after their names - about the behaviour in the mean of the remainder term in the prime number theorem for arithmetical progressions.

The inequality in this result was subsequently converted by Montgomery into an asymptotic formula, which is sometimes described as the Barban-Montgomery theorem because a special case had been derived by Barban. The talk is a survey of work by the speaker and others in the development of the themes of the above theorems. It will describe, inter alia, more accurate versions of these results, other related theorems on prime numbers, and generalizations affecting sequences other than the primes.

Date received: March 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadx-87.