Study on Uniform Distribution in Positive Characteristic | Chapter 1 | Recent Advances in Mathematical Research and Computer Science Vol. 3

 The uniform distribution is an essential topic in classical Diophantine approximation. The estimation of exponential sums using Weyl's criteria and the distribution of real numbers are closely intertwined. We shall find a geometrical description of Carlitz's simple notion of uniform distribution in positive features (see [1]). We employ the Haar measure in this study to offer an exact analogue to Weyl's criteria for positive features. We show that the uniformly distributed modulo 1 for linear forms and polynomial functions is valid. We prove that the set m is uniformly distributed modulo 1 in the Laurent series field, where m extends over all polynomials and is a fixed irrational function.

Author(S) Details

Zhiyong Zheng
School of Mathematics, Renmin University of China, Beijing, P. R. China.

Ziwei Hong
School of Mathematics and Systems Science, Beihang University, Beijing, P. R. China.

Man Chen
Department of Mathematics, South China University of Technology, Guangzhou, P. R. China.

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