The Zeta function, the Arithmetic Lattice and the Quadruple Symmetry
Abstract
The Riemann zeta function $\zeta(s)$ stands at the intersection of analytic number theory, complex analysis, and mathematical physics. This work develops a prime--lattice formulation of $\zeta(s)$ and its modulus square, explores expansions into prime--power series, and examines symmetries of the critical line. Connections are drawn with Voronin’s theorem and propose a framework in which the Riemann Hypothesis emerges naturally from consistency, symmetry, and universality.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Identities
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Figshare
- Publication date
- 1 March 2026
- Language
- EN
- Document type
- Preprint