Additive functions for number systems in function fields

作者：Madritsch Manfred G^*; Thuswaldner Joerg M

来源：Finite Fields and Their Applications, 2010, 16(3): 204-229.

DOI：10.1016/j.ffa.2010.02.002

• Finite fields
• Digit expansions
• Distribution in residue classes
• Weyl sums
• Waring's Problem

Let F(q) be a finite field with q elements and p is an element of F(q)[X, Y]. In this paper we study properties of additive functions with respect to number systems which are defined in the ring F(q)[X, Y]/pF(q)[X, Y]. Our results comprise distribution results, exponential sum estimations as well as a version of Waring's Problem restricted by such additive functions. Similar results have been shown for b-adic number systems as well as number systems in finite fields in the sense of Kovacs and Petho. In the proofs of the results contained in the present paper new difficulties occur because the "fundamental domains" associated to the number systems studied here have a complicated structure.

• 出版日期2010-5