2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/195001We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 dimensional case. The 1d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis.version 3: additional appendix explains how the $ν$ to $1-ν$ duality of Riemann's $ζ(ν)$ follows from a special modular transformation in a massless relativistic theoryMathematical PhysicsStatistical MechanicsHigh Energy Physics - TheoryNumber Theorytext