关于短区间中模q的整数及其逆的分布

On the distribution of integers and their inverses modulo q in a short interval

利用初等方法和解析方法研究了短区间中模q的整数逆的分布性质,建立了短区间中模q的整数逆与Kloosterman和之间的关系,利用Kloosterman和的估计与三角和的性质给出几个较强的渐近公式,所得结果表明该类和式具有较好的分布性质.

By using elementary and analytic methods, the distributive properties of integers and their inverses modulo q in a short interval are discussed. A relationship between inverses modulo q in short interval and Kloosterman sums is established. By using the estimates for Kloosterman sums and properties of trigonometric sums, some sharp asymptotic formulas are given. The results obtained in this paper show that this kind of sums has good distributive properties.