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arXiv · 2510.01896

Quantitative growth of multi-recurrence sequences

Clemens Fuchs·Armand Noubissie
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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.

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Clemens Fuchs, Armand Noubissie. 2025-10-02. Quantitative growth of multi-recurrence sequences. https://arxiv.org/abs/2510.01896

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