Thomas Krause

Euler Products, the Reflection s ↔ 1−s, and Zeta Values at Integers: A Self-Contained Toolkit for the Zeta Anchors of Classical Physics

Many dimensionless prefactors of classical physics are values of the Riemann zeta function at integers: π⁴/15 (Stefan–Boltzmann), π²/720 (Casimir), 2ζ(3) (photon number density), π²/3 (Lorenz number) and ζ(3/2) (Bose–Einstein condensation). This paper collects the mathematics nee...

First Shells of Prime Ideals in Cyclotomic Lattices: E8, the Leech Lattice and a Facet Criterion

Several classical lattices are free modules of rank one over a ring of cyclotomic integers: E8 over Z[ζ30], the Leech lattice over Z[ζ35], and the root lattices A2, D4, A4, A_{p−1} and Z^{2^k} over Z[ζ_h], where h is the Coxeter number. In such a lattice every principal prime ide...