On the p-adic valuations of values of Legendre polynomials

2025/05/13 by Alekseyev, Max A., Amdeberhan, Tewodros, Shallit, Jeffrey +1
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.08935

Abstract

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.

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