Explicit bounds for products of primes in AP

Balasubramanian, Ramachandran; Ramaré, Olivier; Srivastav, Priyamvad

doi:10.1090/mcom/3853

Explicit bounds for products of primes in AP
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by Ramachandran Balasubramanian, Olivier Ramaré and Priyamvad Srivastav HTML | PDF

Math. Comp. 92 (2023), 2381-2411 Request permission

Abstract:

For all $q\ge 2$ and for all invertible residue classes $a$ modulo $q$, there exists a natural number that is congruent to $a$ modulo $q$ and that is the product of exactly three primes, all of which are below $(10^{15}q)^{5/2}$.

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