On the maximal multiplicity of long zero-sum free sequences over $C_p\oplus C_p$

Abstract

In this paper, we point out that the method used in [Acta Arith. 128(2007) 245-279] can be modified slightly to obtain the following result. Let $\epsilon \in (0,\frac{1}{4})$ and $c>0$, and let $p$ be a sufficiently large prime depending on $\epsilon$ and $c$. Then every zero-sumfree sequence $S$ over $C_p\oplus C_p$ of length $|S|\ge 2p-c\sqrt{p}$ contains some element at least $\lfloor p^{\frac{1}{4}-\epsilon }\rfloor$ times.