On Lehmer's Conjecture for Polynomials and for Elliptic Curves
Number Theory
2010-08-24 v1
Abstract
A number of authors have proven explicit versions of Lehmer's conjecture for polynomials whose coefficients are all congruent to 1 modulo m. We prove a similar result for polynomials f(X) that are divisible in (Z/mZ)[X] by a polynomial of the form 1+X+...+X^n for some n > \epsilon*deg(f). We also formulate and prove an analogous statement for elliptic curves.
Cite
@article{arxiv.1008.3649,
title = {On Lehmer's Conjecture for Polynomials and for Elliptic Curves},
author = {Joseph H. Silverman},
journal= {arXiv preprint arXiv:1008.3649},
year = {2010}
}
Comments
22 pages