On the number of subgroups of the group ℤ_m₁ × ℤ_m₂ with m₁m₂≤ x such that m₁m₂ is a k-th power

2025/04/01 by Yankun Sui, Dan Liu, Sui, Yankun +3
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.00331

openalex publication_date 2025/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Bbb Z_m be the additive group of residue classes modulo m and s(m₁,m₂) denote the number of subgroups of the group \Bbb Z_m₁× \Bbb Z_m₂, where m₁ and m₂ are arbitrary positive integers. We consider sums of type ∑_\substackm₁m₂≤ x m₁m₂∈ N_ks(m₁,m₂), where N_k is the set of k-th power of natural numbers. In particular, we deduce asymptotic formulas with k=2 and k=3.

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