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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 5, Pages 145–170 (Mi izv4053)  

This article is cited in 12 scientific papers (total in 13 papers)

On the distribution 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: We prove the existence of the limit density distribution for normalized Frobenius numbers with three arguments. The density is found explicitly.

Keywords: Frobenius numbers, Kloosterman sums, continued fractions.

DOI: https://doi.org/10.4213/im4053

Full text: PDF file (635 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2010, 74:5, 1023–1049

Bibliographic databases:

UDC: 511.335+511.336+517.524
MSC: 11D85, 11D04
Received: 14.10.2008
Revised: 23.06.2009

Citation: A. V. Ustinov, “On the distribution of Frobenius numbers with three arguments”, Izv. RAN. Ser. Mat., 74:5 (2010), 145–170; Izv. Math., 74:5 (2010), 1023–1049

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  • https://doi.org/10.4213/im4053
  • http://mi.mathnet.ru/eng/izv/v74/i5/p145

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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. V. Shchur, Ya. Sinai, A. Ustinov, “Limiting distribution of Frobenius numbers for $n=3$”, J. Number Theory, 129:11 (2009), 2778–2789  crossref  mathscinet  zmath  isi  scopus
    2. I. S. Vorobev, “Eksperimentalnoe issledovanie problemy Frobeniusa dlya trekh argumentov”, Dalnevost. matem. zhurn., 11:1 (2011), 3–9  mathnet  elib
    3. A. V. Ustinov, “Geometric proof of Rødseth's formula for Frobenius numbers”, Proc. Steklov Inst. Math., 276 (2012), 275–282  mathnet  crossref  mathscinet  isi  elib  elib
    4. Shparlinski I.E., “Modular hyperbolas”, Jap. J. Math., 7:2 (2012), 235–294  crossref  mathscinet  zmath  isi  elib  scopus
    5. Aliev I., Fukshansky L., Henk M., “Generalized Frobenius numbers: bounds and average behavior”, Acta Arith., 155:1 (2012), 53–62  crossref  mathscinet  zmath  isi  elib  scopus
    6. Strömbergsson A., “On the limit distribution of Frobenius numbers”, Acta Arith., 152:1 (2012), 81–107  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. V. Ustinov, “Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals”, Sb. Math., 204:5 (2013), 762–779  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. J. Marklof, A. Strömbergsson, “Diameters of random circulant graphs”, Combinatorica, 33:4 (2013), 429–466  crossref  mathscinet  zmath  isi  scopus
    9. A. I. Bufetov, B. M. Gurevich, K. M. Khanin, F. Cellarosi, “The Abel Prize award to Ya. G. Sinai”, Russian Math. Surveys, 69:5 (2014), 931–956  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. A. V. Ustinov, “On Points of the Modular Hyperbola under the Graph of a Linear Function”, Math. Notes, 97:2 (2015), 284–288  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. W. M. Schmidt, “Integer matrices, sublattices of $\mathbb Z^m$, and Frobenius numbers”, Monatsh. Math., 178:3 (2015), 405–451  crossref  mathscinet  zmath  isi  scopus
    12. 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
    13. 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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