Primes and prime ideals in short intervals

Abstract

We prove the analog of Cramér's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based mainly on the inertia property of the counting functions of primes and prime ideals.

minor change to Proposition 2

References in corpus (2)

• Explicit smoothed prime ideals theorems under GRH
• Primes in explicit short intervals on RH

Cited by in corpus (3)

• Standard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory
• Explicit Short Intervals for Primes in Arithmetic Progressions on GRH
• Short-interval sector problems for CM elliptic curves