Multiplicative independence and bounded height
Některé věty týkající se rozkladu mnohočlenů jedné proměnné
New methods providing high degree polynomials with small Mahler measure.
Nonreciprocal algebraic numbers of small Mahler's measure
We prove that there exist at least cd⁵ monic irreducible nonreciprocal polynomials with integer coefficients of degree at most d whose Mahler measures are smaller than 2, where c is some absolute positive constant. These polynomials are constructed as nonreciprocal divisors of some Newman hexanomials , where the integers 1 ≤ r₁ < ⋯ < r₅ ≤ d satisfy some restrictions including for j = 1,2,3,4. This result improves the previous lower bound cd³ and seems to be closer to the correct value of...
Nonreciprocal algebraic numbers of small measure
The main result of this paper implies that for every positive integer there are at least nonconjugate algebraic numbers which have their Mahler measures lying in the interval . These algebraic numbers are constructed as roots of certain nonreciprocal quadrinomials.
Nonstandard arithmetic of iterated polynomials.
On a polynomial conjecture of Pál Turán
On a problem of Győry and Schinzel concerning polynomials
On a question of Lehmer
On a question of Lehmer and the number of irreducible factors of a polynomial
On a theorem of Bauer and some of its applications
On Alternatives of Polynomial Congruences
What should be assumed about the integral polynomials in order that the solvability of the congruence for sufficiently large primes p implies the solvability of the equation in integers x? We provide some explicit characterizations for the cases when are binomials or have cyclic splitting fields.
On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan
We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the -transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses, in the...
On approximate roots of a polynomial.
On certain algebraic curves related to polynomial maps
On characters and polynomials
On cubic factors of certain trinominals.
On cyclotomic polynomials with coefficients.
On Kronecker's elimination theory.
On normal binomials