| _version_ | 1866901458540036096 |
|---|---|
| author | Gokul P |
| author_facet | Gokul P |
| contents | <p>This paper introduces the <strong>Gokul's <em>Divisor Lattice Model</em></strong>, a discrete self-adjoint framework revealing the arithmetic origin of the Riemann symmetry. <strong>Gokul’s Divisor Density Law</strong> states that the total divisor density of all positive<br>integers is <strong>ζ(1)</strong>, and its spectral constant is<strong> Euler’s constant γ</strong>.The model is built from the divisor and forbidden-divisor densities, forming a compact Hilbert–Schmidt operator whose spectrum exhibits mirror balance around ½. Euler’s constant γ acts as the spectral phase aligning the local and global components of the lattice. Analytical proofs and numerical tests confirm bounded, real, and symmetric behavior of the normalized spectral field (10⁻⁴–10⁻³ amplitude range). The results demonstrate how the divisor lattice inherently reproduces the functional symmetry ζ(s)=ζ(1−s) without analytic continuation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17562848 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Gokul's Self-Adjoint Divisor Lattice: A Discrete Arithmetic Origin of the Riemann Symmetry Gokul P Mathematics Mathematical analysis Mathematical logic <p>This paper introduces the <strong>Gokul's <em>Divisor Lattice Model</em></strong>, a discrete self-adjoint framework revealing the arithmetic origin of the Riemann symmetry. <strong>Gokul’s Divisor Density Law</strong> states that the total divisor density of all positive<br>integers is <strong>ζ(1)</strong>, and its spectral constant is<strong> Euler’s constant γ</strong>.The model is built from the divisor and forbidden-divisor densities, forming a compact Hilbert–Schmidt operator whose spectrum exhibits mirror balance around ½. Euler’s constant γ acts as the spectral phase aligning the local and global components of the lattice. Analytical proofs and numerical tests confirm bounded, real, and symmetric behavior of the normalized spectral field (10⁻⁴–10⁻³ amplitude range). The results demonstrate how the divisor lattice inherently reproduces the functional symmetry ζ(s)=ζ(1−s) without analytic continuation.</p> |
| title | Gokul's Self-Adjoint Divisor Lattice: A Discrete Arithmetic Origin of the Riemann Symmetry |
| topic | Mathematics Mathematical analysis Mathematical logic |
| url | https://doi.org/10.5281/zenodo.17562848 |