НОВЫЕ ФОРМУЛЫ, СВЯЗАННЫЕ С АНАЛИТИЧЕСКОЙ ТЕОРИЕЙ ЧИСЕЛ, И ИХ ПРИЛОЖЕНИЕ К СТАТИСТИЧЕСКОЙ ФИЗИКЕ

Теоретическая и математическая физика. 2018. Т. 196. № 1. С. 161–166.

Maslov V.

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.

Keywords: Bose–Einstein distribution, Распределение Бозе-Эйнштейна, аналитическая теория чисел, analytic number theory, Fermi–Dirac distribution, распределение Ферми-Дирака, Gentile distribution, self-consistent equation, specific energy jump, распределение Джентиле, самосогласованное уравнение, скачок удельной энергии