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 ℱ(N) = {s/r : r,s ∈ ℤ, gcd(r,s) = 1, N ≥ r > s ≥ 1} of Farey fractions of order N (only fractions s/r with gcd(r,m) = 1 are considered).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-2,
author = {Igor E. Shparlinski},
title = {Exponential Sums with Farey Fractions},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {57},
year = {2009},
pages = {101-107},
zbl = {1272.11036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-2}
}
Igor E. Shparlinski. Exponential Sums with Farey Fractions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 101-107. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-2/