On the growth of hypergeometric sequences
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918107668283392 |
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| author | Kenison, George Konieczny, Jakub Luca, Florian Scoones, Andrew Shirmohammadi, Mahsa Worrell, James |
| author_facet | Kenison, George Konieczny, Jakub Luca, Florian Scoones, Andrew Shirmohammadi, Mahsa Worrell, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the growth of hypergeometric sequences Kenison, George Konieczny, Jakub Luca, Florian Scoones, Andrew Shirmohammadi, Mahsa Worrell, James Number Theory Formal Languages and Automata Theory 11B37 (Primary), 68Q45 (Secondary) 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. |
| title | On the growth of hypergeometric sequences |
| topic | Number Theory Formal Languages and Automata Theory 11B37 (Primary), 68Q45 (Secondary) |
| url | https://arxiv.org/abs/2507.22437 |