Probabilistic Galois theory in function fields

Entin, Alexei; Popov, Alexander

doi:10.1016/j.ffa.2024.102466

Finite Fields and Their Applications

2024

DOI: 10.1016/j.ffa.2024.102466

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Probabilistic Galois theory in function fields

Alexei Entin,

Alexander Popov

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2024

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Galois groups of random polynomials over the rational function field

Entin

2024

Journal of London Math Soc

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For a fixed prime power and natural number , we consider a random polynomial with drawn uniformly and independently at random from the set of all polynomials in of degree . We show that with probability tending to 1 as the Galois group of over is isomorphic to , where is cyclic, and are small quantities with a simple explicit dependence on . As a corollary we deduce that as . Thus, we are able to overcome the versus ambiguity in the most natural restricted coefficients random polynomial model over , which has not been achieved over so far.

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Galois groups of random polynomials over the rational function field

Entin

2024

Journal of London Math Soc

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Probabilistic Galois theory in function fields

Cited by 1 publication

References 10 publications

Galois groups of random polynomials over the rational function field

Galois groups of random polynomials over the rational function field

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