本项目拟研究加法基与和集中相关问题.具体有以下几方面的研究内容:(1)研究与Erdos-Turan猜想密切相关的加法基,重点应用线性丢番图方程理论构造一些稀薄基和稠密基;(2)研究一些代数结构的分拆及其相应的表示函数;(3)研究Abel群上和集与限制和集个数的下界, 并揭示加法基与某些和集问题的联系.这些研究内容在加法数论中占有十分重要的地位.项目组在此领域已有一定的工作积累,相关研究结果已发表在Acta Arith.,J. Number Theory,Discrete Math.等期刊上.预期成果将进一步丰富加法数论领域的研究.

In this project, we will study additive bases and related problems in sumsets. The detailed study of the project are as follows:(1)Study additive bases which closely related to Erdos-Turan conjecture. In particular, we will use the theory of the linear diophantine equation to construct some thin bases and dense bases; (2)Study partitions of some algebraic structures and their representation functions; (3)Study the lower bound of the number of sumsets and restricted sumsets in some Abel groups; reveal the relation between the additive bases and some sumset problems.These research contents have had very important impact in additive number theory. The project team has some accumulation in this field, the related research results have been published in Acta Arith., J. Number Theory, Discrete Math., and so on. The expected results will further enrich the study of additive number theory.