Open AccessExplicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis
Author(s) -
Anne-Maria Ernvall-Hytönen,
Neea Palojärvi
Publication year - 2022
Publication title -
mathematics of computation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.95
H-Index - 103
eISSN - 1088-6842
pISSN - 0025-5718
DOI - 10.1090/mcom/3691
Subject(s) - mathematics , algorithm , prime (order theory) , riemann hypothesis , arithmetic , combinatorics , pure mathematics
We prove an explicit error term for the ψ ( x , χ ) \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.