English

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.

Keywords

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

R2 v1 2026-07-01T04:25:28.215Z