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arXiv · 2507.22437

On the growth of hypergeometric sequences

George Kenison·Jakub Konieczny·Florian Luca·Andrew Scoones·Mahsa Shirmohammadi·James Worrell
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Abstract

Hypergeometric sequences obey first-order linear recurrence relations with polynomial coefficients and are commonplace throughout the mathematical and computational sciences. For certain classes of hypergeometric sequences, we prove linear growth estimates on their Weil heights. We give an application of our effective results towards the Membership Problem from Computer Science. Recall that Membership asks to procedurally determine whether a specified target is an element of a given recurrence sequence.

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George Kenison, Jakub Konieczny, Florian Luca, Andrew Scoones, Mahsa Shirmohammadi, James Worrell. 2025-07-30. On the growth of hypergeometric sequences. https://arxiv.org/abs/2507.22437

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