Open AccessCyclotomic Expressions for Representation Functions
Author(s) -
Charles Hélou
Publication year - 2019
Publication title -
uniform distribution theory
Language(s) - English
Resource type - Journals
eISSN - 2309-5377
pISSN - 1336-913X
DOI - 10.2478/udt-2019-0008
Subject(s) - modulo , mathematics , representation (politics) , natural number , function (biology) , integer (computer science) , computation , discrete mathematics , pure mathematics , combinatorics , algebra over a field , algorithm , computer science , programming language , evolutionary biology , politics , political science , law , biology
Given a subset A of the natural numbers = {0, 1, 2, ···} (resp. of the ring / N of residue classes modulo a positive integer N ), we introduce certain sums of roots of unity associated with A . We study some of their properties, and we use them to obtain new expressions for the classical functions that characterize A , i.e. of the representation function, the counting function and the characteristic function of A . We also give an example of computations of the representation function using such expressions.