arminstraub.com

Gessel-Lucas congruences for sporadic sequences

Gessel-Lucas congruences for sporadic sequences
Armin Straub — Monatshefte für Mathematik — Volume 203, 2024, Pages 883-898

Abstract

For each of the \(15\) known sporadic Apéry-like sequences, we prove congruences modulo \(p^2\) that are natural extensions of the Lucas congruences modulo \(p\). This extends a result of Gessel for the numbers used by Apéry in his proof of the irrationality of \(\zeta(3)\). Moreover, we show that each of these sequences satisfies two-term supercongruences modulo \(p^{2r}\). Using special constant term representations recently discovered by Gorodetsky, we prove these supercongruences in the two cases that remained previously open.

Download

LinkSizeDescriptionHits
302.93 KB Preprint (PDF, 17 pages) 473

BibTeX

@article{gessel-lucas-2024,
    author = {Armin Straub},
    title = {Gessel--Lucas congruences for sporadic sequences},
    journal = {Monatshefte für Mathematik},
    year = {2024},
    volume = {203},
    pages = {883--898},
    doi = {10.1007/s00605-023-01894-3},
}