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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 4, Pages 125–184 (Mi izv7302)  

This article is cited in 3 scientific papers (total in 3 papers)

The mean value of Frobenius numbers with three arguments

D. Frolenkov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We get an asymptotic formula for the mean value of Frobenius numbers with three arguments when averaged with respect to three parameters.

Keywords: Frobenius numbers, exponential sums.

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


DOI: https://doi.org/10.4213/im7302

Full text: PDF file (792 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2012, 76:4, 760–819

Bibliographic databases:

UDC: 511.335+511.336
MSC: 11D07, 11D45, 11L07
Received: 28.02.2011
Revised: 14.06.2011

Citation: D. Frolenkov, “The mean value of Frobenius numbers with three arguments”, Izv. RAN. Ser. Mat., 76:4 (2012), 125–184; Izv. Math., 76:4 (2012), 760–819

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/izv/v76/i4/p125

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. W. M. Schmidt, “Integer matrices, sublattices of $\mathbb Z^m$, and Frobenius numbers”, Monatsh. Math., 2015  crossref  mathscinet  isi  scopus
    2. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. I. S. Vorob'ev, “On the Frobenius problem for three arguments”, Sb. Math., 207:6 (2016), 816–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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