On the $p$-adic valuations of values of Legendre polynomials

Fuente: arXiv
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Bibliographic Details
Main Authors: Alekseyev, Max A., Amdeberhan, Tewodros, Shallit, Jeffrey, Vukusic, Ingrid
Format: Preprint
Published: 2025
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author Alekseyev, Max A.
Amdeberhan, Tewodros
Shallit, Jeffrey
Vukusic, Ingrid
author_facet Alekseyev, Max A.
Amdeberhan, Tewodros
Shallit, Jeffrey
Vukusic, Ingrid
contents We prove an explicit formula for the $p$-adic valuation of the Legendre polynomials $P_n(x)$ evaluated at a prime $p$, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017.
format Preprint
id arxiv_https___arxiv_org_abs_2505_08935
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the $p$-adic valuations of values of Legendre polynomials
Alekseyev, Max A.
Amdeberhan, Tewodros
Shallit, Jeffrey
Vukusic, Ingrid
Number Theory
We prove an explicit formula for the $p$-adic valuation of the Legendre polynomials $P_n(x)$ evaluated at a prime $p$, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017.
title On the $p$-adic valuations of values of Legendre polynomials
topic Number Theory
url https://arxiv.org/abs/2505.08935