IV.D310 — Epstein zeta structure

The Epstein zeta function Z(s; i*iota_tau) = sum'_{(m,n) in Z^2} (m^2 + n^2*iota_tau^2)^{-s} for Re(s) > 1 is the regularized total breathing energy over all modes of the rectangular lattice Z + i*iota_tau*Z, with iota_tau = 2/(pi+e) as the shape ratio of T^2.