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

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 $\varepsilon \in (0,\frac 14)$ and $c>0$, and let $p$ be a sufficiently large prime depending on $\varepsilon$ and $c$. Then every zero-sumfree sequence $S$ over $C_p\oplus C_p$ of length $|S|\geq 2p-c\sqrt{p}$ contains some element at least $\lfloor p^{\frac14-\varepsilon}\rfloor$ times.