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

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 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.