What question did this study set out to answer?

This research aims to provide a complete proof of the Riemann Hypothesis through advanced mathematical constructs.

June 4, 2026Open Access

Proof of the Riemann Hypothesis via Euler Product Linearization and Self-Adjoint Operator Recursion

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Randomized trial demonstrates a unique infinite-dimensional operator's spectrum matches Riemann zeros, implying the hypothesis holds.

This research aims to provide a complete proof of the Riemann Hypothesis through advanced mathematical constructs.
Developed a sequence of finite-dimensional self-adjoint matrices equivalent to the truncated Riemann xi function.
Applied mathematical induction to show eigenvalues converge to the squares of non-trivial zeros of the Riemann zeta function.
Extended finite-dimensional results to the infinite-dimensional case using the monotone convergence theorem.
Established that eigenvalues of self-adjoint matrices converge to the squares of imaginary parts of non-trivial Riemann zeros.
Proved existence of a unique infinite-dimensional self-adjoint operator whose spectrum matches the Riemann zeros.
Concluded that all non-trivial zeros of the Riemann zeta function have real part 1/2, confirming the Riemann Hypothesis.

Jianning Yang (2026) studied this question.

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June 4, 2026Open Access

View Full Paper

Ask AI

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Authors

Randomized trial demonstrates a unique infinite-dimensional operator's spectrum matches Riemann zeros, implying the hypothesis holds.

This research aims to provide a complete proof of the Riemann Hypothesis through advanced mathematical constructs.
Developed a sequence of finite-dimensional self-adjoint matrices equivalent to the truncated Riemann xi function.
Applied mathematical induction to show eigenvalues converge to the squares of non-trivial zeros of the Riemann zeta function.
Extended finite-dimensional results to the infinite-dimensional case using the monotone convergence theorem.
Established that eigenvalues of self-adjoint matrices converge to the squares of imaginary parts of non-trivial Riemann zeros.
Proved existence of a unique infinite-dimensional self-adjoint operator whose spectrum matches the Riemann zeros.
Concluded that all non-trivial zeros of the Riemann zeta function have real part 1/2, confirming the Riemann Hypothesis.

Jianning Yang (2026) studied this question.

View Full Paper

Ask AI

Bookmark