Integral zeros of a polynomial with linear recurrences as coefficients

2021/03/10 by Clemens Fuchs, Sebastian Heintze · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Advanced Differential Equations and Dynamical Systems

paper · doi:10.1016/j.indag.2021.03.001

Abstract

Let K be a number field, S a finite set of places of K, and OS be the ring of S-integers. Moreover, let Gn(0)Zd+⋯+Gn(d−1)Z+Gn(d)be a polynomial in Z having simple linear recurrences of integers evaluated at n as coefficients. Assuming some technical conditions we give a description of the zeros (n,z)∈N×OS of the above polynomial. We also give a result in the spirit of Hilbert irreducibility for such polynomials.

Citations

• The zero multiplicity of linear recurrence sequences

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• Quantitative growth of multi-recurrences

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