Explicit Short Intervals for Primes in Arithmetic Progressions on GRH

TL;DR

This paper provides explicit bounds for the distribution of primes in arithmetic progressions assuming the generalized Riemann hypothesis, extending Cramér's theorem with concrete numerical results.

Contribution

It offers explicit versions of Cramér's theorem for primes in arithmetic progressions under GRH, with precise bounds and conditions.

Findings

Explicit bounds for primes in arithmetic progressions derived

Results depend on the validity of GRH

Enhanced understanding of prime distribution in progressions

Abstract

We prove explicit versions of Cram\'er's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.