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math.NT2022
Probabilistic Galois Theory -- The Square Discriminant Case
Lior Bary-Soroker, Or Ben-Porath, Vlad Matei
The 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 polynomi…
math.NT2022
Ramified covers of abelian varieties over torsion fields
Lior Bary-Soroker, Arno Fehm, Sebastian Petersen
We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of . In particular, we prove that every elliptic curve over…
math.NT2022
Hilbert's irreducibility theorem via random walks
Lior Bary-Soroker, Daniele Garzoni
Let be a connected linear algebraic group over a number field , let be a finitely generated Zariski dense subgroup of and let be a thin set, in…