What question did this study set out to answer?

This research aims to establish a new geometric framework for understanding the Riemann Hypothesis using a consistent three-dimensional extension of the complex number system.

July 15, 2026Open Access

A New Geometric Framework for the Riemann Hypothesis via an Extended Three-Dimensional Number System

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Authors

FOFlorin OreviceanuFan Noli University

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Implication

Framework paper develops a three-dimensional extension of complex numbers to examine the Riemann Hypothesis, suggesting new structures and analysis methods.

Key Points

This research aims to establish a new geometric framework for understanding the Riemann Hypothesis using a consistent three-dimensional extension of the complex number system.
Introduced a three-dimensional extension of the complex number system, incorporating new algebraic elements.
Proved consistency of the axiom system relative to ZFC through explicit model construction.
Analyzed the properties of the Riemann zeta function and its derivatives within this new framework.
The axiom system is proven consistent (Theorem 1).
At genuine zeros on the critical line, the t-directional derivative of the completed Xi function is purely imaginary (Theorem 2).
The Riemann Hypothesis is shown to be equivalent to the condition that all genuine zeros have purely imaginary t-directional derivatives (Theorem 4).

Cite This Study

Florin Oreviceanu (2026) studied this question.

synapsesocial.com/papers/6a57239488b21df8754803cc https://doi.org/10.5281/zenodo.21347326

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Implication

Framework paper develops a three-dimensional extension of complex numbers to examine the Riemann Hypothesis, suggesting new structures and analysis methods.

A New Geometric Framework for the Riemann Hypothesis via an Extended Three-Dimensional Number System

Discussion

Member takes

Implication

Key Points

Cite This Study

A New Geometric Framework for the Riemann Hypothesis via an Extended Three-Dimensional Number System

Discussion

Member takes

Implication

Key Points

Cite This Study

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