Is a bivariate polynomial with ± 1 coefficients irreducible? Very likely!

Lior Bary-Soroker; Gady Kozma

doi:10.1142/S1793042117500488

Is a bivariate polynomial with ± 1 coefficients irreducible? Very likely!

Lior Bary-Soroker, Gady Kozma

Tel Aviv University, Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the probability of a random polynomial in two variables of degree n and with ± 1 coefficients to be irreducible tends to 1 as n → ∞.

Original language	English
Pages (from-to)	933-936
Number of pages	4
Journal	International Journal of Number Theory
Volume	13
Issue number	4
DOIs	https://doi.org/10.1142/S1793042117500488
State	Published - 1 May 2017

Keywords

Bivariate polynomials
Irreducible polynomials
Probability
Restricted coefficients

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1142/S1793042117500488

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title = "Is a bivariate polynomial with ± 1 coefficients irreducible? Very likely!",

abstract = "We prove that the probability of a random polynomial in two variables of degree n and with ± 1 coefficients to be irreducible tends to 1 as n → ∞.",

keywords = "Bivariate polynomials, Irreducible polynomials, Probability, Restricted coefficients",

author = "Lior Bary-Soroker and Gady Kozma",

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N2 - We prove that the probability of a random polynomial in two variables of degree n and with ± 1 coefficients to be irreducible tends to 1 as n → ∞.

AB - We prove that the probability of a random polynomial in two variables of degree n and with ± 1 coefficients to be irreducible tends to 1 as n → ∞.

KW - Bivariate polynomials

KW - Irreducible polynomials

KW - Probability

KW - Restricted coefficients

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DO - 10.1142/S1793042117500488

M3 - مقالة

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JO - International Journal of Number Theory

JF - International Journal of Number Theory

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Is a bivariate polynomial with ± 1 coefficients irreducible? Very likely!

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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