Exponential Sums with Farey Fractions
Volume 57 / 2009
Bulletin Polish Acad. Sci. Math. 57 (2009), 101-107
MSC: 11B57, 11L07.
DOI: 10.4064/ba57-2-2
Abstract
For positive integers and N, we estimate the rational exponential sums with denominator m over the reductions modulo m of elements of the set {\cal F}(N) = \{ s/r : r,s \in {\mathbb Z},\, \gcd(r,s) = 1, \, N\ge r > s \ge 1\} of Farey fractions of order N (only fractions s/r with \gcd(r,m)=1 are considered).
