Low-Degree Factors of Random Polynomials View Full Text


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Article Info

DATE

2018-06-23

AUTHORS

Sean O’Rourke, Philip Matchett Wood

ABSTRACT

We study the probability that a monic polynomial with integer coefficients has a low-degree factor over the integers, which is equivalent to having a low-degree algebraic root. It is known in certain cases that random polynomials with integer coefficients are very likely to be irreducible, and our project can be viewed as part of a general program of testing whether this is a universal behavior exhibited by many random polynomial models. Our main result shows that pointwise delocalization of the roots of a random polynomial can be used to imply that the polynomial is unlikely to have a low-degree factor over the integers. We apply our main result to a number of models of random polynomials, including characteristic polynomials of random matrices, where strong delocalization results are known. More... »

PAGES

1076-1104

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  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10959-018-0839-8

    DOI

    http://dx.doi.org/10.1007/s10959-018-0839-8

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