Probabilistic Galois Theory: The square discriminant case

Author:

Bary‐Soroker Lior1ORCID,Ben‐Porath Or1,Matei Vlad12

Affiliation:

1. School of Mathematical Sciences Tel Aviv University Tel Aviv Israel

2. Institute of Mathematics of the Romanian Academy Bucharest Romania

Abstract

AbstractThe paper studies the probability for a Galois group of a random polynomial to be . We focus on the so‐called large box model, where we choose the coefficients of the polynomial independently and uniformly from . The state‐of‐the‐art upper bound is , due to Bhargava. We conjecture a much stronger upper bound , and that this bound is essentially sharp. We prove strong lower bounds both on this probability and on the related probability of the discriminant being a square.

Funder

Israel Science Foundation

Publisher

Wiley

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