A Study On The Measure Of Pseudorandom Subsets

In the last decades,numerous papers have been written on pseudorandom measures of subsets,many works like the construction of pseudorandom subsets and randomness analysis are included in those papers.In this paper,depending on the number theory and algebra,we study the connection between pseudoran-dom measures of subsets,introduce measure for multi-dimensional pseudoran-dom subsets,and construct large families of multi-dimensional pseudorandom subsets.Results are as follows:Firstly,we build a link between the Gowers norm and the pseudorandom measure.By using combinatorics,character,character sum,we get that "good"pseudorandom subsets must have "small" Gowers norm,and its converse propo-sition untenable.Based on the link,we also give a detail analysis for conjectures presented by W.T.Gowers.Then we obtain a condition for pseudorandom subset of degree L(k)to contain an arithmetic progression of length k.Secondly,we study the connection between pseudorandom measures of multi-dimensional subsets,construct a family of multi-dimensional pseudoran-dom subsets.By introducing measure for multi-dimensional pseudorandom sub-sets,we study the connection between measures of different orders.Finally,Large families of multi-dimensional pseudorandom subsets are given by using the quadratic character in finite field.