Zeta Zeros as Emergent Modes in a Noncommutative Spectral Network
Year: 2025
Type: article
Abstract: The Hilbert-Pólya conjecture proposes that the nontrivial zeros of the Rie- mann zeta function arise as the eigenvalues of a self-adjoint operator. While recent numerical constructions of one-dimensional Hilbert-Pólya Operators (HPOs) have achieved high-precision spectral alignment with zeta zeros, they do not explain the irregular spacing and statistical properties exhibited by the zeta spectrum. In this work, we construct a family of nonlocal, noncommutative spectral operators whose modal frequencies exhibit GUE-like spacing statistics and bounded residuals when compared to the zeta zeros. We show that the zeta spectrum may be emergent not from a linear self-adjoint sequence but from a higher-order spectral network with modal interactions and frequency tension. This network perspective suggests a new structural foundation for understanding the origin of the zeta zeros.
Author: Li, Y.Y.N.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893190276
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