On the growth of hypergeometric sequences
Number Theory
2025-07-31 v1 Formal Languages and Automata Theory
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.
Cite
@article{arxiv.2507.22437,
title = {On the growth of hypergeometric sequences},
author = {George Kenison and Jakub Konieczny and Florian Luca and Andrew Scoones and Mahsa Shirmohammadi and James Worrell},
journal= {arXiv preprint arXiv:2507.22437},
year = {2025}
}
Comments
22 pages