Chebotarev density theorem in short intervals for extensions of Fq(T)

Lior Bary-Soroker, Ofir Gorodetsky, Taelin Karidi, Will Sawin

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


An old open problem in number theory is whether the Chebotarev density theorem holds in short intervals. More precisely, given a Galois extension E of Q with Galois group G, a conjugacy class C in G, and a 1 ≥ ϵ > 0, one wants to compute the asymptotic of the number of primes x ≤ p ≤ x+xϵ with Frobenius conjugacy class in E equal to C. The level of difficulty grows as ϵ becomes smaller. Assuming the Generalized Riemann Hypothesis, one can merely reach the regime 1 ≥ ϵ > 1/2. We establish a function field analogue of the Chebotarev theorem in short intervals for any ϵ > 0. Our result is valid in the limit when the size of the finite field tends to ∞ and when the extension is tamely ramified at infinity. The methods are based on a higher dimensional explicit Chebotarev theorem and applied in a much more general setting of arithmetic functions, which we name G-factorization arithmetic functions.

Original languageEnglish (US)
Pages (from-to)597-628
Number of pages32
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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