Quantitative growth of multi-recurrences

2026/07/01 by Clemens Fuchs, Armand Noubissie
Mathematics · Physics and Astronomy · Computer Science · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #semigroups and automata theory

paper · pdf · doi:10.1016/j.jnt.2026.05.017

Abstract

In 1982, Schlickewei and Van der Poorten claimed that any multi-recurrence sequence has, essentially, maximal possible growth rate. Fourty years later, Fuchs and Heintze provided a non-effective proof of this statement. In this paper, we prove a quantitative version of that result by giving an explicit upper bound for the maximal possible growth rate of a multi-recurrence. Moreover, we also give a function field analogue of the result, answering a question posed by Fuchs and Heintze when proving a bound on the growth of multi-recurrences in number fields.

Citations

• On the Euler Function of Linearly Recurrence Sequences
• On the growth of multi-recurrences
• A function field variant of Pillai's problem
• Integral zeros of a polynomial with linear recurrences as coefficients
• On composite lacunary polynomials and the proof of a conjecture of Schinzel
• Linear Equations in Variables which Lie in a Multiplicative Group
• The zero multiplicity of linear recurrence sequences
• ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

Related

• Quantitative growth of multi-recurrence sequences
• On the growth of multi-recurrences
• On the growth of recurrence sequences
• Quantitative growth of linear recurrences
• ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS