St. Petersburg Mathematical Journal

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ISSN 1547-7371(e) ISSN 1061-0022(p)

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

Author(s): A. V. Ustinov
Translated by: N. B. Lebedinskaya
Original publication: Algebra i Analiz, tom 20 (2008), nomer 5.
Journal: St. Petersburg Math. J. 20 (2009), 813-836.
MSC (2000): Primary 11L05, 11L07
Posted: July 21, 2009
MathSciNet review: 2492364
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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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