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To construct an operator-theoretic framework for studying non-trivial zeros of the Riemann zeta function using explicit test functions.

May 26, 2026Open Access

From Local Curvature to the Weil Functional: An Explicit Construction

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To construct an operator-theoretic framework for studying non-trivial zeros of the Riemann zeta function using explicit test functions.
Constructed an explicit family of admissible Schwartz-class test functions for the Weil functional.
Derived a prime-side decomposition linking zero sums to local curvature.
Analyzed convergence of the diagonal energy series and provided numerous lemmas.
Proved the admissibility of the test functions in Lagarias' formulation of the Weil criterion.
Established strict positivity of the renormalized prime weights, with elementary algebraic proofs.
Showed diagonal energy series converges with a numerical approximation of D ≈ 9.470.

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Develops an operator-theoretic framework to explore zero distributions in the Riemann zeta function, revealing connections to local curvature.

Ulrich Tehrani (2026) studied this question.

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Develops an operator-theoretic framework to explore zero distributions in the Riemann zeta function, revealing connections to local curvature.