Work

Curvature of the Normalized Totient Function and Prime Gap Structures

Year: 2025

Type: article

Abstract: This work analyzes the normalized Euler totient function I(n)=φ(n)/log⁡nI(n) = \varphi(n)/\log nI(n)=φ(n)/logn and its second discrete differences to study prime gap structures. Computational results show that primes tend to correspond to local minima of curvature, suggesting new heuristic models of prime distribution stability. This curvature method complements probabilistic prime gap theories and provides a testable classical framework for prime regularity analysis.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15285176

Author: Fernandes, Ricardo Miguel Machado

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6893358743

FWCI:

Cites:

Cited by:

Related to: