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Mat. Zametki, 2016, Volume 100, Issue 2, paper published in the English version journal (Mi mz11334)  

This article is cited in 4 scientific papers (total in 4 papers)

Papers published in the English version of the journal

Bose–Einstein Distribution as a Problem of Analytic Number Theory: The Case of Less than Two Degrees of Freedom

V. P. Maslovab, V. E. Nazaikinskiibc

a National Research University Higher School of Economics, Moscow, Russia
b Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
c Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia

Abstract: The problem of finding the number and the most likely shape of solutions of the system $\sum_{j=1}^\infty\lambda_{j}n_{j}\le M$, $\sum_{j=1}^\infty n_j=N$, where $\lambda_j,M,N>0$ and $N$ is an integer, as $M,N\to\infty$, can naturally be interpreted as a problem of analytic number theory. We solve this problem for the case in which the counting function of $\lambda_j$ is of the order of $\lambda^{d/2}$, where $d$, the number of degrees of freedom, is less than two.

Keywords: Bose–Einstein distribution, inverse problem on abstract primes, arithmetic semigroup, zeta function, integral logarithm.


English version:
Mathematical Notes, 2016, 100:2, 245–255

Bibliographic databases:

Document Type: Article
Received: 26.03.2016

Citation: V. P. Maslov, V. E. Nazaikinskii, “Bose–Einstein Distribution as a Problem of Analytic Number Theory: The Case of Less than Two Degrees of Freedom”, Math. Notes, 100:2 (2016), 245–255

Citation in format AMSBIB
\Bibitem{MasNaz16}
\by V.~P.~Maslov, V.~E.~Nazaikinskii
\paper Bose–Einstein Distribution as a Problem of Analytic Number Theory: The Case of Less than Two Degrees of Freedom
\jour Math. Notes
\yr 2016
\vol 100
\issue 2
\pages 245--255
\mathnet{http://mi.mathnet.ru/mz11334}
\crossref{https://doi.org/10.1134/S0001434616070191}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3545147}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000382193300019}
\elib{http://elibrary.ru/item.asp?id=27141411}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84983732405}


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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. P. Maslov, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Volume and Entropy in Abstract Analytic Number Theory and Thermodynamics”, Math. Notes, 100:6 (2016), 828–834  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. P. Maslov, “Large negative numbers in number theory, thermodynamics, information theory, and human thermodynamics”, Russ. J. Math. Phys., 23:4 (2016), 510–528  crossref  mathscinet  zmath  isi  scopus
    3. V. P. Maslov, “Topological phase transitions in the theory of partitions of integers”, Russ. J. Math. Phys., 24:2 (2017), 249–260  crossref  mathscinet  zmath  isi  scopus
    4. De Gregorio P., Rondoni L., “Microcanonical Entropy, Partitions of a Natural Number Into Squares and the Bose-Einstein Gas in a Box”, Entropy, 20:9 (2018), 645  crossref  isi
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