March 3, 2026Open Access

A Conjecture on the Riemann Zeros from the Ibaguner Fractal Operator (IFO) Master Equation

Key Points

The conjecture connects the non-trivial zeros of the Riemann zeta function to the Ibaguner constant D.
A fractal dimension of D = 0.3715(9) suggests a unique structure to the distribution of these zeros.
Using the Ibaguner formalism, the conjecture presents a new geometric view of the Riemann Hypothesis.
This framework implies a deeper interplay between quantum gravity and the nature of prime numbers.

Abstract

We present a conjecture linking the universal fractal dimension D = 0.3715(9) (the Ibaguner constant) to the distribution of the non-trivial zeros of the Riemann zeta function. The conjecture arises from the IFO Master Equation, a proposed unified framework incorporating quantum gravity, gauge theories, and fractal space-time. Under the assumption that the IFO formalism correctly describes the large-scale structure of spacetime and the small-scale distribution of prime numbers, the Riemann Hypothesis is reinterpreted as a geometric necessity: all non-trivial zeros lie on the line (s) = D, and their spacing distribution exhibits a fractal dimension D.

A Conjecture on the Riemann Zeros from the Ibaguner Fractal Operator (IFO) Master Equation

Key Points

Abstract

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