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New results in comparative prime number theory
by
Kevin Ford
University of South Carolina
Coauthors: Richard Hudson
Let \pi(q, a;x) denote the number of prime numbers <= x and lying in the progression a modulo q. Set \Delta(q, a, b;x)=\pi(q, a;x)-\pi(q, b;x). The study of the behavior of the functions \Delta(q, a, b;x) has been termed ``comparative prime number theory''. We present some new results, both theoretical and computational, concerning the location of sign changes of \Delta(q, a, b;x) for general q, and give some specifics in the case q=8.
Date received: April 13, 1999
Copyright © 1999 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 # cacu-08.