Some remarks on the paper "Rank of mapping tori and companion matrices" by G. Levitt and V. Metaftsis

Francesco Amoroso (1) , Umberto Zannier (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 SNS - Scuola Normale Superiore di Pisa

Let A be a matrix in GL_d(Z) of infinite order. In a recent paper, G. Levitt and V. Metaftsis prove that for any sufficiently large n the matrix A^n is not conjugated to a companion matrix. We first prove a local version of this theorem. Then, we give an effective statement, using linear form in logarithms. We also discuss several related problems.

Domaines: Théorie des nombres [math.NT]

Francesco Amoroso, Umberto Zannier. Some remarks on the paper "Rank of mapping tori and companion matrices" by G. Levitt and V. Metaftsis. 2011. ⟨hal-00637093v1⟩