On Lehmer's Conjecture for Polynomials and for Elliptic Curves

arXiv1008.3649MaRDI QIDQ6220311

Publication date: 21 August 2010

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.

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Heights (11G50) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) (11J97)

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