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Математические заметки, 2016, том 100, выпуск 2, статья опубликована в англоязычной версии журнала
(Mi mzm11334)
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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Статьи, опубликованные в английской версии журнала
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
Аннотация:
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.
Ключевые слова:
Bose–Einstein distribution, inverse problem on abstract primes,
arithmetic semigroup, zeta function, integral logarithm.
Поступило: 26.03.2016
Образец цитирования:
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
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mzm11334
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