Harmonic analysis on the positive rationals: computation of character sums

Abstract

The authors carry out detailed calculations of group character sums attached to the multiplicative representation of positive rationals by pairs of sequences \(an+b\), \(An+B\), \(n = 1, 2 \dots \), with the integer coefficients a, b, A, B satisfying \(a>0\), \(A>0\), \(aB - Ab \ne 0\). Non-intuitive examples are given.