On the $p$-adic valuations of values of Legendre polynomials
Number Theory
2025-05-15 v1
Abstract
We prove an explicit formula for the -adic valuation of the Legendre polynomials evaluated at a prime , and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017.
Cite
@article{arxiv.2505.08935,
title = {On the $p$-adic valuations of values of Legendre polynomials},
author = {Max A. Alekseyev and Tewodros Amdeberhan and Jeffrey Shallit and Ingrid Vukusic},
journal= {arXiv preprint arXiv:2505.08935},
year = {2025}
}