oalogo2  

AUTHOR(S):

Yang I. Cao

 

TITLE

Paradoxes or Contradictions? Exploring the Riemann-Zeta Function and Riemann Hypothesis by Euler’s Identity and Category Theory

pdf PDF

ABSTRACT

The research studies the Riemann Zeta Function (RZF) and the Riemann hypothesis (RH) with the Harmonic Series by Euler’s identity and category theory. I attempt to simplify the RZF by a metric space with geometric analysis. I further explore the nondiscrete mathematical relations of Euler’s identity and the basic trigonometric functions in the analytic geometric space, and some morphisms are constructed. The study demonstrated the viability of the three-dimensional coordinate construction with its topological relations to be further explored and justified. The current form of the solutions corroborates with the nontrivial zero solutions, and further tests on the RH will need a paradigm shift on the preliminary results.

KEYWORDS

non-algebraic numbers; morphism; injection; zero morphism; discrete and nondiscrete mathematics; unit sphere; powers and exponents; structuralism

 

Cite this paper

Yang I. Cao. (2025) Paradoxes or Contradictions? Exploring the Riemann-Zeta Function and Riemann Hypothesis by Euler’s Identity and Category Theory. International Journal of Applied Physics, 10, 52-58

 

cc.png
Copyright © 2024 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0