English

A Note on the Linnik's constant

Number Theory 2010-10-19 v1

Abstract

Let P(a,q)P(a,q) be the least prime in the arithmetic progression {na(mod q)}\{n\equiv a(mod\ q)\}. In this note, when qq has bounded cubic part and (a,q)=1(a,q)=1, we combine the Heath-Brown's method and the Burgess's bounds for L-functions to obtain P(a,q)q4.5. P(a,q)\ll q^{4.5}.

Keywords

Cite

@article{arxiv.1010.3544,
  title  = {A Note on the Linnik's constant},
  author = {Zaizhao Meng},
  journal= {arXiv preprint arXiv:1010.3544},
  year   = {2010}
}
R2 v1 2026-06-21T16:29:56.294Z