Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593441 | Journal of Number Theory | 2016 | 18 Pages |
Abstract
In this paper, we show that various kinds of integer polynomials with prescribed properties of their roots have positive density. For example, we prove that almost all integer polynomials have exactly one or two roots with maximal modulus. We also show that for any positive integer n and any set of n distinct points symmetric with respect to the real line, there is a positive density of integer polynomials of degree n, height at most H and Galois group SnSn whose roots are close to the given n points.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Artūras Dubickas, Min Sha,