We investigate the approximation to the number of primes in arithmetic progressions given by Vaughan [7]. Instead of averaging the expected error term over all residue classes to modules in a given range, here we only consider subsets of arithmetic progressions that satisfy additional congruence conditions and provide asymptotic approximations.

arithmetic progressions, asymptotic approximations.

Received: January 8, 2023; Accepted: February 9, 2023; Published: February 23, 2023

How to cite this article: Claus Bauer, On Vaughan’s approximation in restricted sets of arithmetic progressions, JP Journal of Algebra, Number Theory and Applications 60(2) (2023), 97-116. http://dx.doi.org/10.17654/0972555523007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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