Wolstenholme primes and group determinants of cyclic groups

2023/10/31 by Cid Reyes-Bustos, Naoya Yamaguchi, Reyes-Bustos, Cid +3
Mathematics · #11A41 #11C20 #20C15 #65F40 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2311.00010

openalex publication_date 2023/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Wolstenholme prime is a prime number p ≥ 5 that divides the numerator of the Bernoulli number B_p-3. A number of equivalent definitions for Wolstenholme primes are known, mostly related to congruences of harmonic sums or binomial coefficients. In this paper, we introduce an equivalent definition of Wolstelholme primes related the number of terms in the group determinant of cyclic groups, and equivalently, the cardinality of certain sets of restricted partitions.

Related

• Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862--2012)
• Wilson's and Wolstenholme's Theorems
• Remark on a determinant involving prime numbers
• Principal Specialization of Monomial Symmetric Polynomials and Group Determinants of Cyclic Groups
• Determinants of Representations of Coxeter Groups