arXiv subjects

Zhengqiang Li

Publications and source records attributed to Zhengqiang Li.

5 recordsLinked to original sources

arXiv2026

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory

The prime numbers and the non-trivial zeros of the Riemann zeta function are globally linked by the explicit formula of analytic number theory. Whether they share a hidden, scale-by-scale geometric symmetry has remained unexplored. We address this by measuring the joint fractal structure of a prime residue class (p=1,5,9,13 mod 16) and the zero distribution of zeta(s). Our central finding is that the duality measure K = 1/d_P + 1/zeta_R is remarkably stable, varying by only 17% across scales L=100--2000, captured by a finite-size scaling law K(L) = K_IR + a*L^{-b}. After geometric normalization, the data converge to a universal infrared fixed point K_IR = 4 with critical exponent b ~ 0.51, robust across two random-matrix symmetry classes (beta=2,4), echoing Montgomery--Odlyzko universality. We interpret K as a conserved information current between the arithmetic and spectral domains, with the scaling law reflecting a renormalization-group flow from an ultraviolet fixed point K_UV = 11 (Hurwitz's theorem on normed division algebras) to K_IR = 4. The exponent b ~ 1/2 is derived from a variational information action S[I_P, I_Z]. A structural argument for the Riemann Hypothesis emerges: the generator kappa with kappa^2 = ijk = -1 enforces, via exchange symmetry I_P <-> I_Z, the fixed point I_P* = I_Z* = 2, encoding the critical line Re(s) = 1/2. Upgrading this to a rigorous proof is the central open problem. We also explore, in a speculative spirit, whether (K_IR, b, kappa) resonate with quantities in quantum gravity and learning theory, including the Bekenstein--Hawking entropy formula. These analogies define open problems at the interface of number theory, physics, and information science.

math.GM↗

arXiv2026

Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory

This paper investigates a class of deterministic fractals whose construction is governed by arithmetic sequences. We introduce the essential fractal prime set P_{ess} , a variant of the Cantor set constructed using the sequence of prime numbers modulo 4. We compute its Hausdorff dimension, \dim_H(P_{ess}) , and analyze its geometric complexity. In contrast to the classical middle-third Cantor set C_{1/3} , we demonstrate that while both sets are uncountable and share the same cardinality, their differing fractal dimensions (dim_H(C_{1/3}) versus the computed dimension of P_{ess}) reflect a fundamental difference in their geometric complexity. Furthermore, we propose a potential connection between the density of this prime-driven fractal and the distribution of zeros of the Riemann zeta function, formalized through the construction of a fractal zero set Z_F . This framework provides a novel geometric perspective on analytic number theory, illustrating how the fine-scale structure of primes can be encoded in deterministic fractal geometries.

math.GM↗

arXiv2026

A Deterministic Fractal Set Derived from the Sequence of Prime Numbers

We introduce a novel deterministic fractal set PF in the unit interval whose construction is driven by the sequence of prime numbers modulo 16. At each step of the recursive construction, two subintervals are retained based on the residues of consecutive primes, yielding a Cantor-like set with a uniform contraction ratio of 1/16 and a branching number of 2. We prove that PF is a non-empty, compact, nowhere dense set of Lebesgue measure zero. Its Hausdorff dimension and box-counting dimension are both equal to 1 4 . The dimension is universal in the sense that it does not depend on the specific choice of the residue sequence, but only on the branching number and the contraction ratio. A generalization to arbitrary bases and branching numbers is also provided. This construction establishes a rigorous link between number theory and fractal geometry, offering a deterministic fractal whose structure is entirely encoded by the distribution of primes.

math.GM↗

arXiv2019

Global haze aerosol distribution: a direct view by Geofen-5 satellite with 3.3 km spatial resolution

The Directional Polarimetric Camera (DPC) is the first Chinese multi-angle polarized earth observation satellite sensor, which has been launched onboard the GaoFen-5 Satellite in Chinese High-resolution Earth Observation Program. GaoFen-5 runs in a sun-synchronous orbit with the 2-days revisiting period. DPC employed a charge coupled device detection unit, and can realize spatial resolution of 3.3 km under a swath width of 1850 km. Moreover, DPC has 3 polarized channels together with 5 non-polarized bands, and is able to obtain at least 9 viewing angles by continuously capturing series images over the same target on orbit. Based on the Directional Polarization Camera (DPC) onboard GF-5 satellite, the first global high-resolution (3.3 km) map of fine-mode aerosol optical depth (AODf) over land has been obtained together by Aerospace Information Institute, Chinese Academy of Sciences, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences (the manufacturer of DPC sensor) and other institutes. This AODf remote sensing observation dataset has the highest spatial resolution in the world. It can reflect the spatial information of major air pollutants (PM2.5, etc.) and provide critical basic products for "decryption" of global haze distribution.

physics.ao-ph↗

arXiv2019

Study on the spectral reconstruction of typical surface types based on spectral library and principal component analysis

To meet the demanding of spectral reconstruction in the visible and near-infrared wavelength, the spectral reconstruction method for typical surface types is discussed based on the USGS /ASTER spectral library and principal component analysis (PCA). A new spectral reconstructed model is proposed by the information of several typical bands instead of all of the wavelength bands, and a linear combination spectral reconstruction model is also discussed. By selecting 4 typical spectral datasets including green vegetation, bare soil, rangeland and concrete in the spectral range of 400-900 nm, the PCA results show that 6 principal components could characterized the spectral dataset, and the relative reconstructed errors are smaller than 2%. If only 6-7 selected typical bands are employed to spectral reconstruction for all the surface reflectance in 400-900 nm, except that the reconstructed error of green vegetation is about 3.3%, the relative errors of other 3 datasets are all smaller than 1.6%. The correlation coefficients of those 4 datasets are all larger than 0.99, which can effectively satisfy the needs of spectral reconstruction. In addition, based on the spectral library and the linear combination model of 4 common used bands of satellite remote sensing such as 490, 555, 670 and 865 nm, the reconstructed errors are smaller than 8.5% in high reflectance region and smaller than 1.5% in low reflectance region respectively, which basically meet the needs of spectral reconstruction. This study can provide a reference value for the surface reflectance processing and spectral reconstruction in satellite remote sensing research.

eess.IV↗