Dα: A Fractional Spectral Framework for Number Theory and Structural Computation
Year: 2025
Type: article
Abstract: This paper introduces the fractional derivative operator Dα as a versatile mathematical tool for high-precision numerical analysis of complex functions, with applications demonstrated on the non-trivial zeros of the Riemann zeta function ζ(s). We integrate Dα with ad- vanced techniques, including windowed Fourier transforms, short-time Fourier transform (STFT), Caputo fractional derivatives, variational optimization, high-order numerical integration (Gauss-Legendre), and Riemann-Siegel correction. Our method achieves a prediction error of 10−10 for zeros within t ∈[0,100], showcasing Dα’s efficacy across a broad range of analytic functions. While results support the Riemann Hypothesis, our focus is on establishing Dα as a general-purpose tool for numerical analysis in mathematics, offering scalability and preci- sion beyond specific conjectures.
Author: Li, Y.Y.N.
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6930864812
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