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

Yushuang Fan; Linlin Wang; Qinghai Zhong

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

Number Theory 2012-11-26 v1 Combinatorics

Authors: Yushuang Fan , Linlin Wang , Qinghai Zhong

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 $\varepsilon \in (0,\frac 14)$ 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.

Keywords

zero-sum free sequence maximal multiplicity finite abelian group additive combinatorics number theory prime number group structure

Cite

@article{arxiv.1211.5226,
  title  = {On the maximal multiplicity of long zero-sum free sequences over $C_p\oplus C_p$},
  author = {Yushuang Fan and Linlin Wang and Qinghai Zhong},
  journal= {arXiv preprint arXiv:1211.5226},
  year   = {2012}
}

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

Abstract

Keywords

Cite

Related papers