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Mat. Sb., 2012, Volume 203, Number 2, Pages 143–160 (Mi msb7787)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic behaviour of the first moment of the number of steps in the by-excess and by-deficiency Euclidean algorithms

D. Frolenkov

M. V. Lomonosov Moscow State University

Abstract: The first moments for the number of steps in different Euclidean algorithms are considered. For these moments asymptotic formulae with new remainder terms are obtained using refined estimates for sums of fractional parts and some ideas in Selberg's elementary proof of the prime number theorem.
Bibliography: 12 titles.

Keywords: Euclidean algorithms, continued fractions, fractional parts, prime number theorem.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00759-a


DOI: https://doi.org/10.4213/sm7787

Full text: PDF file (500 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:2, 288–305

Bibliographic databases:

Document Type: Article
UDC: 511.335
MSC: Primary 11Y16; Secondary 11A55, 11K50
Received: 04.09.2010 and 14.12.2010

Citation: D. Frolenkov, “Asymptotic behaviour of the first moment of the number of steps in the by-excess and by-deficiency Euclidean algorithms”, Mat. Sb., 203:2 (2012), 143–160; Sb. Math., 203:2 (2012), 288–305

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v203/i2/p143

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  zmath  adsnasa  isi  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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