On the number of ramified primes in specializations of function fields over ℚ

2015/11/08 by Lior Bary‐Soroker, Bary-Soroker, Lior, François Legrand +1
Mathematics · #Meromorphic and Entire Functions #Algebraic Geometry and Number Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1511.02478

Abstract

We study the number of ramified prime numbers in finite Galois extensions of ℚ obtained by specializing a finite Galois extension of ℚ(T). Our main result is a central limit theorem for this number. We also give some Galois theoretical applications.

Related

• The minimal ramification problem for rational function fields over finite fields
• The Tamely Ramified Geometric Quantitative Minimal Ramification Problem
• The number of ramified primes in number fields of small degree
• Specialization results and ramification conditions
• On the local behaviour of specializations of function field extensions