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math.NT2024
Irreducibility of Polynomials with Square Coefficients over Finite Fields
Lior Bary-Soroker, Roy Shmueli
We study a random polynomial of degree over the finite field , where the coefficients are independent and identically distributed and uniformly chosen from the sq…
math.NT2024
On the irreducibility of and other such polynomials
Lior Bary-Soroker, Daniele Garzoni, Vlad Matei
Let be irreducible and let . Under a necessary ramification as…
math.NT2024
Full Galois groups of polynomials with slowly growing coefficients
Lior Bary-Soroker, Noam Goldgraber
Choose a polynomial uniformly at random from the set of all monic polynomials of degree with integer coefficients in the box . The main result of the paper assert…