New Formulas Related to Analytic Number Theory and Their Applications in Statistical Physics

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...

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Bibliographic Details
Published inTheoretical and mathematical physics Vol. 196; no. 1; pp. 1082 - 1087
Main Author Maslov, V. P.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Chemical potential
Integers
Mathematical analysis
Mathematical and Computational Physics
Number theory
Numbers
Organic chemistry
Physics
Physics and Astronomy
Statistical physics
Theoretical
Bose–Einstein distribution
Fermi–Dirac distribution
specific energy jump
analytic number theory
self-consistent equation
Gentile distribution
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Summary: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 μ, 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.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577918070127