English

Primes and prime ideals in short intervals

Number Theory 2017-02-15 v2

Abstract

We prove the analog of Cram\'er'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.

Keywords

Cite

@article{arxiv.1602.02906,
  title  = {Primes and prime ideals in short intervals},
  author = {L. Grenié and G. Molteni and A. Perelli},
  journal= {arXiv preprint arXiv:1602.02906},
  year   = {2017}
}

Comments

minor change to Proposition 2

R2 v1 2026-06-22T12:46:27.779Z