New York Journal of Mathematics
Volume 27 (2021), 1415-1438


Matteo Bordignon

Medium-sized values for the prime number theorem for primes in arithmetic progressions

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Published: October 1, 2021.
Keywords: Primes in arithmetic progressions, explicit results.
Subject: 11N13, 11M06, 11M20.

We give two improved explicit versions of the prime number theorem for primes in arithmetic progressions: the first isolating the contribution of the Siegel zero and the second completely explicit, where the improvement is for medium-sized values of x. This will give an improved explicit Bombieri--Vinogradov-like result for non-exceptional moduli.


I would like to thank my supervisor Tim Trudgian for his help in developing this paper and his insightful comments. I would also like to thank the anonymous reviewer, Kevin O'Bryant and Daniel Johnston for the helpful comments and suggestions.

Author information

Matteo Bordignon:
University of New South Wales Canberra
School of Science
Canberra ACT 2610, Australia