Overdetermined Weil Systems and the Riemann Hypothesis

July 6, 2026Open Access

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Key Points

The research aims to investigate the constraints on non-trivial zeros of the Riemann zeta function using the Weil explicit formula.
Utilized the even test function $h_n^{\mathrm{even}}$ to generate constraints on zeros.
Applied Paley-Wiener theory and Schwarz reflection to analyze the behavior of zeros on the critical line.
Demonstrated linear independence of constraint functions through algebraic elimination.
Established that all non-trivial zeros satisfy $\mathrm{Re}(s)=1/2$.
Proved the linear independence of functions $\{f_k\}_{k=1}^{M}$, leading to a contradiction for $M\geq1$.
Concluded that the only possible value for $M$ is zero, thus confirming the hypothesis.

Explores constraints of non-trivial zeros in the Riemann Hypothesis, indicating key mathematical implications.

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Yifan Zhou (2026) studied this question.

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