M. G. Rukavishnikova, “The Law of Large Numbers for the Sum of the Partial Quotients of a Rational Number with Fixed Denominator”, Mat. Zametki, 2011, Volume 90, Issue 3,Pages <nobr>431

This article is cited in 7 papers

The Law of Large Numbers for the Sum of the Partial Quotients of a Rational Number with Fixed Denominator

M. G. Rukavishnikova^ab

^a Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
^b Far-Eastern State University of Humanities

Abstract: We obtain a nontrivial estimate of the variance of the sum of bounded partial quotients appearing in the continued-fraction expansion of a rational number with fixed denominator. As a consequence, we obtain a law of large numbers for the sum of all partial quotients.

Keywords: law of large numbers, rational number, continued fraction, partial quotient, Euler function, Möbius function, Riemann zeta function.

UDC: 511.36+511.37

Received: 12.02.2009
Revised: 04.12.2010

DOI: 10.4213/mzm8484