An asymptotically tight bound for the Davenport constant

TL;DR

This paper establishes an asymptotically tight bound for the Davenport constant of the direct product of cyclic groups, showing it approaches rn as n grows large, with an extended theorem included.

Contribution

The paper proves an asymptotic formula for the Davenport constant of cyclic group products, extending previous bounds with a precise asymptotic characterization.

Findings

Davenport constant $ ext{D}(C_n^r)$ is asymptotic to rn as n approaches infinity.

Provides an extension of the main theorem to broader cases.

Confirms the tightness of the asymptotic bound for large n.

Abstract

We prove that for every integer $r \ge 1$ the Davenport constant $\mathsf{D}(C^r_n)$ is asymptotic to $rn$ when $n$ tends to infinity. An extension of this theorem is also provided.