# Exponential Sums with Farey Fractions

Bulletin of the Polish Academy of Sciences. Mathematics (2009)

- Volume: 57, Issue: 2, page 101-107
- ISSN: 0239-7269

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topIgor E. Shparlinski. "Exponential Sums with Farey Fractions." Bulletin of the Polish Academy of Sciences. Mathematics 57.2 (2009): 101-107. <http://eudml.org/doc/281171>.

@article{IgorE2009,

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
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).
},

author = {Igor E. Shparlinski},

journal = {Bulletin of the Polish Academy of Sciences. Mathematics},

keywords = {Farey fractions; double exponential sums; Erdős-Turán inequality},

language = {eng},

number = {2},

pages = {101-107},

title = {Exponential Sums with Farey Fractions},

url = {http://eudml.org/doc/281171},

volume = {57},

year = {2009},

}

TY - JOUR

AU - Igor E. Shparlinski

TI - Exponential Sums with Farey Fractions

JO - Bulletin of the Polish Academy of Sciences. Mathematics

PY - 2009

VL - 57

IS - 2

SP - 101

EP - 107

AB -
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).

LA - eng

KW - Farey fractions; double exponential sums; Erdős-Turán inequality

UR - http://eudml.org/doc/281171

ER -

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