Harmonic analysis on the positive rationals: computation of character sums.

The authors carry out detailed calculations of group character sums attached to the multiplicative representation of positive rationals by pairs of sequences a n + b , A n + B , n = 1 , 2 ⋯ , with the integer coefficients a, b, A, B satisfying a > 0 , A > 0 , a B - A b ≠ 0 . Non-intuitive examples are given. [ABSTRACT FROM AUTHOR]