The Geometric Triangle Decomposition of the Riemann Zeta Function

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Authors: Maksim Rakhman, Maksim Rakhman
Cited by: 0

Abstract

We present a geometric framework connecting the trivial zeros of the Riemann zeta function (s = -2n) with the non-trivial zeros (s = 1/2 + it_n) through right triangles with vertex at the origin. We prove that the first angle θ₀ ≈ 81.95° is the strict global maximum (the "brit milah property"), identify inflection points corresponding to prime number deserts, and reinterpret the classical identity |χ(1/2+it)| = 1 as optical impedance matching at the critical line. 9 pages, 7 figures. Computational collaboration with Claude (Anthropic).

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Identities Advanced Mathematical Theories and Applications

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
9 February 2026
Document type
Preprint