On the number of solutions of the congruence 𝑥𝑦≡𝑙 (mod 𝑞) under the graph of a twice continuously differentiable function

Ustinov, A.

doi:10.1090/S1061-0022-09-01074-7

On the number of solutions of the congruence $xy\equiv l\pmod {q}$ under the graph of a twice continuously differentiable function
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by A. V. Ustinov
Translated by: N. B. Lebedinskaya

St. Petersburg Math. J. 20 (2009), 813-836

DOI: https://doi.org/10.1090/S1061-0022-09-01074-7

Published electronically: July 21, 2009

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Abstract:

A result by V. A. Bykovskiĭ (1981) on the number of solutions of the congruence $xy\equiv l\pmod {q}$ 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 Euclidean algorithm is sharpened and extended to the case of Gauss–Kuzmin statistics.

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