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Article

Bose-Einstein distribution as a problem of analytic number theory: The case of less than two degrees of freedom

Mathematical notes. 2016. Vol. 100. No. 1. P. 245-255.
Maslov V. P., Nazaikinskii V. E.

The problem of finding the number and the most likely shape of solutions of the system ∑∞ j=1λjnj ≤ M, ∑∞ j=1 nj = N where λj,M,N > 0 and N is an integer, as M,N →∞, can naturally be interpreted as a problem of analytic number theory. We solve this problem for the case in which the counting function of λj is of the order of λd/2, where d, the number of degrees of freedom, is less than two.