Functional composition of polynomials: indecomposability, Diophantine equations and lacunary polynomials

D Kreso, RF Tichy - arXiv preprint arXiv:1503.05401, 2015 - arxiv.org
… for the indecomposability of polynomials, which haven’t been … lacunary polynomias (polynomials
with few terms), which have received a special attention in the literature on polynomial

[图书][B] Lacunary polynomials over finite fields

L Rédei - 2014 - books.google.com
… decompositions of the form … some lacunary polynomials in F[x], arising in various connections.
These examples will show us that in F[x] we very often have to deal with such polynomials, …

On lacunary polynomial perfect powers

M Giesbrecht, DS Roche - Proceedings of the twenty-first international …, 2008 - dl.acm.org
… t-sparse or lacunary polynomial f is a perfect power, that is, f=h r for some other polynomial h
… a perfect power in time polynomial in the size of the lacunary representation. The algorithm …

Lacunary Polynomial Compositions

A Moscariello - arXiv preprint arXiv:2104.11704, 2021 - arxiv.org
… f(g(X)), depending on the number of terms of both polynomials involved. Schinzel’s … by
studying lacunary polynomials obtained as composition of a Laurent polynomial g(X1,...,…

[PDF][PDF] On common values of lacunary polynomials at integer points.

D Kreso - New York Journal of Mathematics, 2015 - emis.de
… as a functional composition of two polynomials of degree greater than 1) lacunary polynomials.
Of … 0, a polynomial with few terms and large degree cannot have an inner noncyclic …

On lacunary polynomials and a generalization of Schinzel's conjecture

D Dona - 2015 - spectrum.library.concordia.ca
… rather than on the other data leads to some interesting questions regarding in particular
the behaviour of lacunary polynomials under the operation of composition, or in even more …

Explicit bounds for composite lacunary polynomials

C Karolus - Glasnik matematički, 2019 - hrcak.srce.hr
polynomial is fixed. It was conjectured by Erdos that if g is a complex non-constant polynomial
… He also extended the conjecture to compositions f(x) = g(h(x)), claiming that if f has l terms, …

Large deviation principles for lacunary sums

C Aistleitner, N Gantert, Z Kabluchko, J Prochno… - Transactions of the …, 2023 - ams.org
… called a lacunary trigonometric sum, and can be viewed as a random variable defined on
the probability space $\Omega=[0, 1] $ endowed with Lebesgue measure. Lacunary sums are …

Diophantine equations in separated variables and lacunary polynomials

D Kreso - International Journal of Number Theory, 2017 - World Scientific
… The behavior of lacunary polynomials with respect to functional composition is a topic of
independent interest, and has been studied by several authors. In this paper, we utilize known …

[PDF][PDF] Lacunary series as quadratic differentials in conformal dynamics

FP Gardiner, D Sullivan - Contemporary Mathematics, 1994 - repo-archives.ihes.fr
polynomial-like mapping P acting on a plane domain, we denote the forward iterates of P
under composition … this space is identifiable with certain lacunary series. There is an associated …