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Mat. Sb., 2016, Volume 207, Number 6, Pages 53–78 (Mi msb8370)  

On the Frobenius problem for three arguments

I. S. Vorob'ev

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

Abstract: Asymptotic formulae for the mean values of various characteristics of the additive semigroup generated by three positive integers are obtained theoretically, the first of which is a formula for the number of integers not belonging to this semigroup. A numerical experiment is described which validates the results obtained.
Bibliography: 21 titles.

Keywords: continued fractions, Frobenius numbers, Kloostermann sums, double-circuit networks.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-90002 Бел_а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 14-01-90002 Бел_а).


DOI: https://doi.org/10.4213/sm8370

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English version:
Sbornik: Mathematics, 2016, 207:6, 816–840

Bibliographic databases:

Document Type: Article
UDC: 511.335+517.524
MSC: Primary 11D07; Secondary 11Y99
Received: 31.03.2014 and 16.12.2015

Citation: I. S. Vorob'ev, “On the Frobenius problem for three arguments”, Mat. Sb., 207:6 (2016), 53–78; Sb. Math., 207:6 (2016), 816–840

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