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The solution of Arnold's problem on the weak asymptotics of Frobenius numbers with three arguments

A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: It is shown that on the average the Frobenius numbers $f(a,b,c)$ behave like $\frac8\pi\sqrt{abc}$ .
Bibliography: 28 titles.

Keywords: Frobenius numbers, continued fractions, Kloosterman sums.

UDC: 511.336+511.218+511.335

MSC: 11D85, 11D04

Received: 05.08.2008 and 05.01.2009

DOI: 10.4213/sm6547

 English version: Sbornik: Mathematics, 2009, 200:4, 597–627

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