Journal of Algebra, Number Theory: Advances and ApplicationsAuthor's: Zhiyong Zheng, Ziwei Hong and Man Chen
Pages: [17] - [40]
Received Date: April 26, 2019
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100122060
Uniform distribution is an important subject in classical Diophantine
approximation. There is a close connection between the distribution of
real numbers and the estimation of exponential sums via Weyl’s
criteria. Carlitz gave a definition of uniform distribution in
positive characteristic in an elementary way (see [11]), however, we
are going to find a geometrical description. In this paper, we present
a precise analogue to Weyl’s criteria in the case of positive
characteristic by using Haar measure. As an application, we show that
the uniformly distributed modulo 1 for linear forms and for polynomial
functions. In particular, we prove the set 
in the Laurent series field is uniformly
distributed modulo 1, where m extends over all the polynomials
and 
is a fixed irrational function.
uniformly distributed modulo 1, Laurent series field, Haar measure.
