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Littlewood polynomials

Roelfszema, M.T. (2015) Littlewood polynomials. Bachelor's Thesis, Mathematics.

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Abstract

A Littlewood polynomial is a polynomial of which all coefficients are in {-1,1}. The zeros of Littlewood polynomials do not only make a beautiful plot, they also have some fascinating properties. For example the symmetry in the real and imaginary axis and the unit circle and bounds for the absolute value of the zeros. Also, the intersection of the set of zeros of Littlewood polynomials with the set of all zeros of quadratic polynomials with rational coefficients turns out to consist of only 12 elements. We sketch the proofs of two known facts, namely that the closure of the set of zeros of Littlewood polynomials is connected and that all z with |z|^4 between 1/2 and 2 are in that closure.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:05
Last Modified: 15 Feb 2018 08:05
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/12857

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