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The aim is to present a proof strategy for the Riemann Hypothesis based on Q-concavity and a central identity.

March 31, 2026Open Access

Q-Concavity and the Riemann Hypothesis

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The aim is to present a proof strategy for the Riemann Hypothesis based on Q-concavity and a central identity.
Utilized calculus to prove the central identity: dρk = ρk(λ)·∆2rk(λ) dλ.
Established the connection between Q-concavity and monotonicity of the ratio ρk(λ) = rk+1/rk.
Derived Turán inequalities for all k and λ based on Q-concavity.
Confirmed that Q-concavity ∆2rk(λ) < 0 supports the essential identity.
Demonstrated that once Q-concavity is established, the Turán inequalities hold.
Showed that the theorem by Csordas-Varga (1988) provides the necessary foundation for the Riemann Hypothesis.

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The proof outlines Q-concavity's role in establishing the Riemann Hypothesis, connecting key mathematical concepts.

Eugene Sporyshev (2026) studied this question.

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