WANG Xiao-ying, ZHAO Qiu-hong
(Department of Mathematics, Northwest University, Xi′an 710127, Shaanxi, China)
Abstract:
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.
KeyWords:
integer; inverse of an integer; distribution; short interval; asymptotic formulaMR subject classification: 11A07
