Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis

Ernvall-Hytönen, Anne-Maria; Palojärvi, Neea

doi:10.1090/mcom/3691

Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis
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by Anne-Maria Ernvall-Hytönen and Neea Palojärvi HTML | PDF

Math. Comp. 91 (2022), 1317-1365 Request permission

Abstract:

We prove an explicit error term for the $\psi (x,\chi )$ function assuming the Generalized Riemann Hypothesis. Using this estimate, we prove a conditional explicit bound for the number of primes in arithmetic progressions.

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