Geodesic
Exponential Sums with Farey Fractions
Igor E. Shparlinski1
1 Department of Computing Macquarie University Sydney, NSW 2109, Australia
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 2, pp. 101-107

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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).
DOI : 10.4064/ba57-2-2
Keywords: positive integers estimate rational exponential sums denominator reductions modulo elements set cal mathbb gcd farey fractions order only fractions gcd considered

Igor E. Shparlinski 1

1 Department of Computing Macquarie University Sydney, NSW 2109, Australia 
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Igor E. Shparlinski. Exponential Sums with Farey Fractions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 2, pp. 101-107. doi: 10.4064/ba57-2-2

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