Linear recurrence sequences and twisted binary forms

Claude Levesque; Michel Waldschmidt

paper

Linear recurrence sequences and twisted binary forms

arXiv:1802.05154

Abstract

Let $\prod_{i = 1}^{d} (X - α_{i} Y) \in C [X, Y]$ be a binary form and let $ε_{1}, \dots, ε_{d}$ be nonzero complex numbers. We consider the family of binary forms $\prod_{i = 1}^{d} (X - α_{i} ε_{i}^{a} Y)$ , $a \in Z$ , which we write as $X^{d} - U_{1} (a) X^{d - 1} Y + \dots + (- 1)^{d - 1} U_{d - 1} (a) X Y^{d - 1} + (- 1)^{d} U_{d} (a) Y^{d} .$ In this paper we study these sequences $(U_{h} (a))_{a \in Z}$ which turn out to be linear recurrence sequences.

Proceedings of the International Conference on Pure and Applied Mathematics ICPAM-GOROKA 2014, "Contemporary Developments in the Mathematical Sciences as Tools for Scientific and Technological Transformation of Papua New Guinea"