本项目主要研究多项式序列的算术性质和有限Abel群上的子序列和问题。主要内容包括：研究三次级数连续项的最小公倍数的渐近行为；研究与三次级数连续项的最小公倍数相关联的周期算术函数的最小正周期问题；研究四次级数连续项的最小公倍数的渐近行为；研究与四次级数连续项的最小公倍数相关联的最小正周期问题；确定秩为2的有限Abel群上的子序列和不变量 ；研究Jaeger-Linial-Payan-Tarsi猜想.

In this project, we shall mainly investigate arithmetic properties of a polynomial sequence and subsequence sums over finite abelian groups. The main contents are as follows: to explore the asymptotic behavior of the least common multiple of consecutive cubic progression terms; to study the smallest period problems of periodic arithmetic functions associated with the least common multiple of consecutive cubic progression terms; to investigate the asymptotic behavior of the least common multiple of consecutive quartic progression terms; to study the smallest period problems of periodic arithmetic functions associated with the least common multiple of consecutive quartic progression terms; to determine the exact value of subsequence-sums invariant for finite abelian group of rank 2; to explore Jaeger-Linial-Payan-Tarsi conjecture.