Probabilities for absolute irreducibility of multivariate polynomials by the polytope method

Date

2011-01-01

Author

Koyuncu, Fatih
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

91
views

0
downloads

Motivated by the Dubickas's result in [1], which computes the probability of the irreducible polynomials by Eisenstein's criterion for some families of polynomials in Z[x], we calculate the probabilities which represent the ratio of absolutely irreducible multivariate polynomials by the polytope method in some families of polynomials over arbitrary fields.

Subject Keywords

Absolute irreducibility, Polytopes, Multivariate polynomials

URI

https://hdl.handle.net/11511/38175

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-0906-101

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

PERTURBATIONS OF NONASSOCIATIVE BANACH ALGEBRAS Dosi, Anar (Rocky Mountain Mathematics Consortium, 2009-01-01) In this note we prove that if either 21 is a Banach-Jordan algebra or a Banach-Lie algebra then all perturbations of the multiplication in 21 give algebras topologically isomorphic with 21 whenever certain small-dimension cohomology groups associated with 21 are vanishing.
The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace Çakıroğlu, Yağmur; Yayla, Oğuz; Yılmaz, Emrah Sercan (2022-08-01) We present the formula for the number of monic irreducible polynomials of degree n over the finite field F-q where the coefficients of x(n)(-1) and x vanish for n >= 3. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements a is an element of F-qn for which Trace(a) = 0 and Trace(a(-1)) = 0.
Additive polynomials and primitive roots over finite fields Özbudak, Ferruh (2001-01-01) We prove existence of primitive roots with a prescribed nonzero image using the arithmetic of algebraic function fields for a class of polynomials over sufficiently large finite fields.
Bivariate polynomial mappings associated with simple complex Lie algebras Küçüksakallı, Ömer (2016-11-01) There are three families of bivariate polynomial maps associated with the rank-2 simple complex Lie algebras A(2), B-2 congruent to C-2 and G(2). It is known that the bivariate polynomial map associated with A(2) induces a permutation of F-q(2) if and only if gcd(k, q(3) - 1) = I. for s = 1, 2, 3. In this paper, we give similar criteria for the other two families. As an application, a counterexample is given to a conjecture posed by Lidl and Wells about the generalized Schur's problem.
A note on the minimal polynomial of the product of linear recurring sequences Cakcak, E (1999-08-06) Let F be a field of nonzero characteristic, with its algebraic closure, F. For positive integers a, b, let J(a, b) be the set of integers k, such that (x - 1)k is the minimal polynomial of the termwise product of linear recurring sequences sigma and tau in F ($) over bar, with minimal polynomials (x - 1)(a) and (x - 1)(b) respectively. This set plays a crucial role in the determination of the product of linear recurring sequences with arbitrary minimal polynomials. Here, we give an explicit formula to deter...

Citation Formats

F. Koyuncu and F. Özbudak, “Probabilities for absolute irreducibility of multivariate polynomials by the polytope method,” TURKISH JOURNAL OF MATHEMATICS, pp. 367–373, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38175.