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arXiv · 1008.3649

On Lehmer's Conjecture for Polynomials and for Elliptic Curves

Joseph H. Silverman
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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 > ε*deg(f). We also formulate and prove an analogous statement for elliptic curves.

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Joseph H. Silverman. 2010-08-21. On Lehmer's Conjecture for Polynomials and for Elliptic Curves. https://arxiv.org/abs/1008.3649

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