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 Sn whose roots are close to the given n points.
Original language | English |
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Pages (from-to) | 27-44 |
Number of pages | 18 |
Journal | Journal of Number Theory |
Volume | 159 |
DOIs | |
Publication status | Published - 1 Feb 2016 |
Externally published | Yes |
Keywords
- Dominant polynomial
- Integer polynomial
- Polynomial root
- Positive density
- Primary
- Secondary