Additive functions for number systems in function fields

Let Fq be a finite field with q elements and p ∈ Fq[X, Y ]. In this paper we study properties of additive functions with respect to number systems which are defined in the ring Fq[X, Y ]/p Fq[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 Kov´acs and Peth˝o. 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.

• Type: Journal
• Year: 2010
• Where: FFA
• Authors: Manfred G. Madritsch, Jörg M. Thuswaldner
• Keywords: Additive Functions, Exponential Sum Estimations, FFA 2010, Number Systems