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 $m$ 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).
