Moments in the Chebotarev density theorem: non-Gaussian families

2023/01/30 by Régis de la Bretèche, de La Bretèche, Régis, Daniel Fiorilli +3
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2301.12826

openalex publication_date 2023/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate higher moments attached to the Chebotarev Density Theorem. Our focus is on the impact that peculiar Galois group structures have on the limiting distribution. Precisely we consider in this paper the case of groups having a character of large degree. Under the Generalized Riemann Hypothesis, we prove in particular that there exists families of Galois extensions of number fields having doubly transitive Frobenius group for which no Gaussian limiting distribution occurs.

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