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math.NT2019★ 1 cited
Discriminants of Fields Generated by Polynomials of Given Height
Rainer Dietmann, Alina Ostafe, Igor E. Shparlinski
We obtain upper bounds for the number of monic irreducible polynomials over of a fixed degree and a growing height for which the field generated by one of its r…
math.NT2019★ 1 cited
Perfect powers in value sets and orbits of polynomials
Alina Ostafe, Lukas Pottmeyer, Igor E. Shparlinski
We show the finiteness of perfect powers in orbits of polynomial dynamical systems over an algebraic number field. We also obtain similar results for perfect powers represented by…
math.NT2019
Dynamical irreducibility of polynomials modulo primes
László Mérai, Alina Ostafe, Igor E. Shparlinski
For a class of polynomials , which in particular includes all quadratic polynomials, and also trinomials of some special form, we show that, under some natural…