1.12. Riemann function The Riemann function () is defined by () = n=1 1 n a. Interpret this expression as the partition function

1.12. Riemann function The Riemann function ζ(β) is defined by

ζ(β) =

∞



n=1 1

nβ

a. Interpret this expression as the partition function in the canonical ensemble of a quantum system and identify the discrete spectrum of the energies.

b. Compute the density of states and the entropy of the quantum system. Interpret the singularity of ζ(β) at β = 1 as a phase transition.