A unified and improved Chebotarev density theorem

Jesse Thorner, Asif Zaman

Research output: Contribution to journalArticlepeer-review


We establish an unconditional effective Chebotarev density theorem that improves uniformly over the well-known result of Lagarias and Odlyzko. As a consequence, we give a new asymptotic form of the Chebotarev density theorem that can count much smaller primes with arbitrary log-power savings, even in the case where a Landau–Siegel zero is present. Our main theorem also interpolates the strongest unconditional upper bound for the least prime ideal with a given Artin symbol as well as the Chebotarev analogue of the Brun–Titchmarsh theorem proved by the authors.

Original languageEnglish (US)
Pages (from-to)1039-1068
Number of pages30
JournalAlgebra and Number Theory
Issue number5
StatePublished - 2019
Externally publishedYes


  • Binary quadratic forms
  • Chebotarev density theorem
  • Distribution of primes
  • Effective
  • Uniform

ASJC Scopus subject areas

  • Algebra and Number Theory


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