Refined Prime Density via Zero Optimization
Year: 2025
Type: article
Abstract: This paper proposes the Refined Prime Density (RPD) standard as a spectral refinement and potential replacement for the classical estimate π(x)/x ≈1/log x from the Prime Number Theorem. We introduce an oscillatory correction function ϕ(x) constructed from Riemann zeros via the explicit formula, with an amplitude parameter k approaching the perfect state k= 1 where residual vanishes, deduced from the Riemann Hypothesis’s zero pair correlation [3], and the residual field δ(x), proposing a novel bounded residual conjecture |δ(x)|< C log x, where C >0 is a theoretical upper bound constant. This provides a more precise model for prime number density with rigorous justification rooted in zero distribution analysis.
Author: Li, Y.Y.N.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6912291055
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