English

Sparser variance for primes in arithmetic progression

Number Theory 2017-06-23 v1

Abstract

We obtain an analog of the Montgomery-Hooley asymptotic formula for the variance of the number of primes in arithmetic progressions. In the present paper the moduli are restricted to the sequences of integer parts [F(n)][F(n)], where F(t)=tcF(t) = t^c (c>1c > 1, c∉Nc \not\in \mathbb{N}) or F(t)=exp((logt)γ)F(t) = \exp\big((\log t)^{\gamma}\big) (1<γ<3/21 < \gamma < 3/2).

Keywords

Cite

@article{arxiv.1706.07319,
  title  = {Sparser variance for primes in arithmetic progression},
  author = {Roger Baker and Tristan Freiberg},
  journal= {arXiv preprint arXiv:1706.07319},
  year   = {2017}
}
R2 v1 2026-06-22T20:26:39.940Z