Geodesic
Sets of the form $\mathscr A+\mathscr B$ and finite continued fractions
Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 537-557

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Estimates are obtained for the number of proper irreducible fractions with denominator $p$ such that an initial and an end segment of their expansion in a continued fraction have bounded partial quotients. These results are connected with an estimate of incomplete Kloosterman sums over sets of the form $\mathscr A+\mathscr B\subset\mathbb Z_p$. Results on the distribution in $\mathbb Z_p$ of the elements of sets of the form $(\mathscr A+\mathscr B)^k$ and $k\cdot(\mathscr A+\mathscr B)^{-1}$ are obtained. Bibliography: 21 titles. 
@article{SM_2007_198_4_a4,
     author = {N. G. Moshchevitin},
     title = {Sets of the form $\mathscr A+\mathscr B$ and finite continued fractions},
     journal = {Sbornik. Mathematics},
     pages = {537--557},
     publisher = {mathdoc},
     volume = {198},
     number = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_4_a4/}
}
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N. G. Moshchevitin. Sets of the form $\mathscr A+\mathscr B$ and finite continued fractions. Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 537-557. http://geodesic.mathdoc.fr/item/SM_2007_198_4_a4/