Polynomials with divisors of every degree

Lola Thompson

Polynomials with divisors of every degree

Number Theory 2011-11-24 v1

Authors: Lola Thompson

Abstract

We consider polynomials of the form t^n-1 and determine when members of this family have a divisor of every degree in Z[t]. With F(x) defined to be the number of such integers up to x, we prove the existence of two positive constants c_1 and c_2 such that $c_1 x/(log x) \leq F(x) \leq c_2 x/(log x).$

Keywords

polynomial theory polynomials over finite fields polynomial roots

Cite

@article{arxiv.1111.5401,
  title  = {Polynomials with divisors of every degree},
  author = {Lola Thompson},
  journal= {arXiv preprint arXiv:1111.5401},
  year   = {2011}
}

Comments

18 pages, to appear in the Journal of Number Theory

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