A variation of q-Wolstenholme's theorem

2020/02/15 by Ji-Cai Liu, Liu, Ji-Cai
Mathematics · #11A07 #11B65 #11T06 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2002.06357

openalex publication_date 2020/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate a variation of q-Wolstenholme's theorem, which extends the q-analogue of Wolstenholme's theorem due to Shi and Pan [Amer. Math. Monthly 114 (2007), 529--531]. The proof makes use of the Ramanujan sum and higher order logarithmic derivatives of cyclotomic polynomials.

Citations

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