Higher-rank cases of Kubertin’s conjecture

Establish Kubertin’s conjectured formula s_{kq}(C_q^r)=(k+r)q−r for prime powers q and ranks r≥4, thereby resolving the cases that remain open after the rank-three results.

Background

The paper places its contribution in the context of Kubertin’s conjecture and states that the conjecture had remained widely open for abelian groups of rank at least three. The paper then resolves every remaining rank-three case, so the unresolved part identified by the paper after its results is the higher-rank regime.

The desired equality is the natural lower-bound formula for generalized Erdős–Ginzburg–Ziv constants of C_q^r. Proving it in ranks at least four would extend the paper’s exact rank-three theorem to the broader family of finite abelian groups of higher elementary rank.