Work

Diophantus' On Polygonal Numbers via Recursive Fractal Dynamics and Prime-Modulated Geometry

Year: 2025

Type: article

Abstract: We rigorously complete Diophantus’ seminal work, On Polygonal Numbers, by scaffolding classical number-theoretic results with modern analytic, algebraic, and computational techniques. This construct extends polygonal number theory through recursive solutions of Pell equations, analytic connections to zeta functions and modular forms, and prime-modulated torsion fields. By incorporating fractal dynamics and geometric deformations, we establish a comprehensive framework for polygonal representations of integers, revealing new structural symmetries and density theorems within the space of polygonal partitions

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15121427

Author: Del Bel, Julian

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6893263286

FWCI:

Cites:

Cited by:

Related to: