Note on the index conjecture in zero-sum theory and its connection to a Dedekind-type sum

Fan Ge

paper

Note on the index conjecture in zero-sum theory and its connection to a Dedekind-type sum

arXiv:1606.01605

Abstract

Let $S = (a_{1}) \dots (a_{k})$ be a minimal zero-sum sequence over a finite cyclic group $G$ . The index conjecture states that if $k = 4$ and $g cd (∣ G ∣, 6) = 1$ , then $S$ has index 1. In this note we study the index conjecture and connect it to a Dedekind-type sum. In particular we reprove a special case of the conjecture when $∣ G ∣$ is prime.

to appear in JNT; may differ slightly from the final version