Geodesic
On the number of solutions of the congruence $xy\equiv l$ $(\operatorname{mod}q)$ under the graph of a twice continuously differentiable function
Algebra i analiz, Tome 20 (2008) no. 5, pp. 186-216 Cet article a éte moissonné depuis la source Math-Net.Ru

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A result by V. A.Bykovskiĭ (1981) on the number of solutions of the congruence $xy\equiv l$ $(\operatorname{mod}q)$ under the graph of a twice continuously differentiable function is refined. As an application, Porter's result (1975) on the mean number of steps in the Euclid algorithm is sharpened and extended to the case of Gauss–Kuzmin statistics.
Keywords: Euclid algorithm, Gauss–Kuzmin statistics, Kloosterman sums. 
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A. V. Ustinov. On the number of solutions of the congruence $xy\equiv l$ $(\operatorname{mod}q)$ under the graph of a twice continuously differentiable function. Algebra i analiz, Tome 20 (2008) no. 5, pp. 186-216. http://geodesic.mathdoc.fr/item/AA_2008_20_5_a7/

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