What question did this study set out to answer?

The aim is to test the algebraic-spectral framework against the requirements of analytic number theory regarding the Riemann Hypothesis.

August 6, 2026Open Access

Spectral Boundaries of the Divisor Operator Framework: A Fredholm Determinant No-Go Theorem for the Riemann Hypothesis

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Demonstrates a limit on the divisor operator framework for the Riemann Hypothesis, implying the model cannot represent the Zeta function.

The aim is to test the algebraic-spectral framework against the requirements of analytic number theory regarding the Riemann Hypothesis.
Constructed a Fredholm determinant associated with the bounded inverse divisor operator.
Applied rigorous analytic number theory requirements including the Euler product and functional equation.
Performed trace expansion calculations to analyze the operator's structure.
Demonstrated that the operator yields an irreducible non-prime residual structure.
Showed that the model fails to reproduce the Euler product, thus cannot represent the Zeta function.
Validated that the spectral density simulates the Riemann-von Mangoldt law.

YOUSEF MUHAMMAD ALSAGHIR Al YOUSEF (2026) studied this question.

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