A Coherence-Driven Spectral Method for High-Precision Computation of Riemann Zeta Zeros (LUSTRO: Local Unitary Spectrum Through Relational Optimization)
Year: 2025
Type: article
Abstract: LUSTRO: A Coherence-Driven Spectral Method for High-Precision Computation of Riemann Zeta Zeros LUSTRO (Local Unitary Spectrum Through Relational Optimization) is a novel algorithm for computing zeros of the Riemann zeta function on the critical line Re(s) = 1/2 with arbitrary precision. Key results: Computes the first nontrivial Riemann zero ρ₁ = 1/2 + i·14.134725... to 1512 verified digits in 104 seconds Sub-quadratic scaling O(d^1.7) in digit count Validated against OEIS A058303 and Odlyzko's tables Package contents: Full paper (LaTeX source + PDF) Python implementation with gmpy2/mpmath backends Complete 1512-digit result with convergence data The method combines the Riemann-Siegel formula for efficient Z(t) evaluation with coherence-based Newton iteration and adaptive precision scaling.
Author: Spychalski, Robert
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7106836439