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On lacunary polynomials and a generalization of Schinzel’s conjecture

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On lacunary polynomials and a generalization of Schinzel’s conjecture

Dona, Daniele (2015) On lacunary polynomials and a generalization of Schinzel’s conjecture. Masters thesis, Concordia University.

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Abstract

Some interesting questions can be posed regarding the maximum number of terms of a polynomial when dealing with particular operations: for example, Rényi and Erdős asked whether there is a bound on the number of terms of h(x) depending only on the number of terms of h(x)^2. In the last decade, positive answers have been found for very general situations: a conjecture by Schinzel on the case of g(h(x)) having few terms for some complex polynomial g has been proven in [8], and an even more general case where h(x) satisfies F(x,h(x))=0 for some complex polynomial F in two variables has been proven in [2]; moreover, the bounds obtained are dependent very poorly on g and F.
We are exposing here the proof of Schinzel’s conjecture contained in [8] and of its aforementioned generalized form contained in [2]; we also give explicit formulas and procedures to calculate the bounds themselves, which were lacking in the original papers.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Dona, Daniele
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:July 2015
Thesis Supervisor(s):Iovita, Adrian
ID Code:980332
Deposited By: DANIELE DONA
Deposited On:04 Nov 2015 20:29
Last Modified:18 Jan 2018 17:51
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