Some congruences for generalized harmonic numbers and binomial coefficients with roots of unity

Walid Kehila ()
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Walid Kehila: Faculty of Mathematics, LATN Laboratory

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 467-478

Abstract: Abstract In this paper, we will establish a formula that relates the product $$\prod _{\omega ^n=1} {\omega x-1 \atopwithdelims ()p-1}$$ ∏ ω n = 1 ω x - 1 p - 1 to generalized and homogeneous multiple harmonic sums, this would allow us to derive new identities and congruences. The congruences considered in this paper are congruences in $$\mathbb {C}_p$$ C p which are also valid in $$\mathbb {Z}_p$$ Z p and $$\mathbb {Z}$$ Z . In order to prove these congruences, we employ well-known theorems for symmetric functions and harmonic numbers.

Keywords: Generalized harmonic numbers; Binomial coefficient; p-adic numbers; Roots of unity (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00056-1

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