Abstract:
A result by V. A.Bykovskiĭ (1981) on the number of solutions of the congruence $xy\equiv l$$(\operatorname{mod}q)$ under the graph of a twice continuously differentiable function is refined. As an application, Porter's result (1975) on the mean number of steps in the Euclid algorithm is sharpened and extended to the case of Gauss–Kuzmin statistics.
Citation:
A. V. Ustinov, “On the number of solutions of the congruence $xy\equiv l$$(\operatorname{mod}q)$ under the graph of a twice continuously differentiable function”, Algebra i Analiz, 20:5 (2008), 186–216; St. Petersburg Math. J., 20:5 (2009), 813–836
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\by A.~V.~Ustinov
\paper On the number of solutions of the congruence $xy\equiv l$ $(\operatorname{mod}q)$ under the graph of a~twice continuously differentiable function
\jour Algebra i Analiz
\yr 2008
\vol 20
\issue 5
\pages 186--216
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\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 5
\pages 813--836
\crossref{https://doi.org/10.1090/S1061-0022-09-01074-7}
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