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To establish a new zero-free region for the Riemann zeta function along the critical line, σ = 1/2.

March 15, 2026Open Access

A Zero-Free Region for ζ(s) via Transverse Tidal Curvature and L² Energy Constraints

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To establish a new zero-free region for the Riemann zeta function along the critical line, σ = 1/2.
Proving an explicit constant C∞(η) related to conditional zeros.
Using tidal dichotomy to analyze transverse curvature effects.
Applying Parseval's identity and Montgomery–Vaughan large sieve inequality for bounding energy.
The derived zero-free region is asymptotically stronger than classical Vinogradov–Korobov bounds.
Numerical verification for the first 50 nontrivial zeros shows improved constraints.

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The proof demonstrates a zero-free region for the Riemann zeta function on the critical line, highlighting its implications.

Thierry Marechal (2026) studied this question.

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