Primitive Factorisation of the Evans Lattice Zeta

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Authors: Pavel Kramarenko-Byrd
Cited by: 15
References: 4

Abstract

Research Note 38 in the "Geometry of the Critical Line" programme. This note proves a canonical factorisation of the leading-WKB Evans lattice zeta. The integer scaling action (n,m') → (dn,dm') partitions the lattice into primitive orbits (gcd(n,m') = 1) and their integer multiples. Standard Möbius inversion gives Z_Evans(s) = ζ(2s) · Z_prim(s), where Z_prim is the primitive lattice zeta and ζ(2s) is the Riemann zeta function at argument 2s. The factorisation is verified numerically to six significant figures. It shows that the Riemann zeta function is already present as the common-scaling multiplicity factor of the Evans lattice. The geometric factor Z_prim(s) carries the pole at s = 1; the arithmetic factor ζ(2s) carries the pole at s = 1/2. The factorisation identifies where the arithmetic content lives inside the carrier geometry, but does not by itself extract it — that requires the operator-algebraic quotient.

Fields of Study & Subjects

Quantum Mechanics and Non-Hermitian Physics Mathematical functions and polynomials Algebraic and Geometric Analysis

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
8 April 2026
Language
EN
Document type
Preprint