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TMF, 2018, Volume 196, Number 1, Pages 161–166 (Mi tmf9597)  

New formulas related to analytic number theory and their applications in statistical physics

V. P. Maslovab

a National Research University "Higher School of Economics," Moscow, Russia
b Ishlinsky Institute for Problems in Mechanics, RAS, Moscow, Russia

Abstract: Since the deep paper by Bohr and Kalckar in 1938, it has been known that the Ramanujan formula in number theory is related to statistical physics and nuclear theory. From the early 1970s, there have been attempts to generalize number theory from the space of integers to the space of rational numbers, i.e., to construct a so-called analytic number theory. In statistical physics, we consider parameters such as the volume $V$, temperature $T$, and chemical potential $\mu$, which are not integers and are consequently related to analytic number theory. This relation to physical concepts leads us to seek new relations in analytic number theory, and these relations turn out to be useful in statistical physics.

Keywords: analytic number theory, Bose–Einstein distribution, Fermi–Dirac distribution, Gentile distribution, self-consistent equation, specific energy jump.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations AAAA-A17-117021310377-1
This research was supported by the Federal Target Program (contract No. AAAA-A17-117021310377-1).


DOI: https://doi.org/10.4213/tmf9597

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English version:
Theoretical and Mathematical Physics, 2018, 196:1, 1082–1087

Bibliographic databases:

Received: 21.03.2018

Citation: V. P. Maslov, “New formulas related to analytic number theory and their applications in statistical physics”, TMF, 196:1 (2018), 161–166; Theoret. and Math. Phys., 196:1 (2018), 1082–1087

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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