The mean number of steps in the Euclidean algorithm with least absolute value remainders

DOI10.1134/S0001434609010179zbMath1208.11014OpenAlexW2055912915MaRDI QIDQ1033905

Alexey Ustinov

Publication date: 10 November 2009

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434609010179

zbMATH Keywords

continued fractionEuclidean algorithmEuclidean algorithm with least absolute value remainderGauss--Kuzmin statistics

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Continued fractions and generalizations (11J70) Continued fractions (11A55) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (4)

CONTINUED FRACTIONS WITH ODD PARTIAL QUOTIENTS ⋮ Modular hyperbolas ⋮ The average length of finite continued fractions with fixed denominator ⋮ The mean number of steps in the Euclidean algorithm with odd partial quotients

Cites Work

• Unnamed Item
• Euclidean algorithms are Gaussian
• On a theorem of Heilbronn

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