On Lehmer's Conjecture for Polynomials and for Elliptic Curves

Details On Lehmer's Conjecture for Polynomials and for Elliptic Curves On Lehmer's Conjecture for Polynomials and for Elliptic Curves

2010-08-21

arxiv.org/abs/1008.3649v1

Mathematics

Number Theory

22 pages

Scientific paper

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.

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