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, 2008, Volume 20, Issue 5,Pages 186

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Research Papers

On the number of solutions of the congruence $xy\equiv l$ $(\operatorname{mod}q)$ under the graph of a twice continuously differentiable function

A. V. Ustinov

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.

Keywords: Euclid algorithm, Gauss–Kuzmin statistics, Kloosterman sums.

MSC: 11L05, 11L07

Received: 12.12.2007