论文标题
在某些多项式版本上，有关亚组的总和问题
On some polynomial version on the sum-product problem for subgroups
论文作者
论文摘要
我们概括了有关质阶有限场的乘法组的亚组的两个结果。特别是，如果变量$ x $和$ y $属于残留物的乘法组的子组$ g $，则在一定条件下获得多项式$ p（x，y）$的基数的下限。同样，该论文包含了这样的证据，表明如果可以将亚组$ g $作为一组$ p（x，y）$的值表示，其中$ x \ in a $ in $ y \ in B $中的$ y \，则$ y \ in b $，那么sets $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a和$ b $的基础（在$ a $ a $ a）中是$ a $ a $ a $ a $和$ b $的（在$ b $中）是接近$ g $ $ g $ $ g $ g $ g $ g $ g $的根源。
We generalize two results about subgroups of multiplicative group of finite field of prime order. In particular, the lower bound on the cardinality of the set of values of polynomial $P(x,y)$ is obtained under the certain conditions, if variables $x$ and $y$ belong to a subgroup $G$ of the multiplicative group of the filed of residues. Also the paper contains a proof of the result that states that if a subgroup $G$ can be presented as a set of values of the polynomial $P(x,y)$, where $x\in A$, and $y\in B$ then the cardinalities of sets $A$ and $B$ are close (in order) to a square root of the cardinality of subgroup $G$.
