A Quantitative Coercivity Framework for a Mellin Convolution Operator and a Structured Route Toward the Riemann Hypothesis
A Quantitative Coercivity Framework for a Mellin Convolution Operator and a Structured Route Toward the Riemann Hypothesis
We construct a coercivity-based analytic framework for a Mellin convolution operator Tσ withkernel Kσ(x) = Γ(1−σ+ilog x), acting on L2(w) under a log–smooth weight. Three componentsform the core: (i) principal symbol positivity, (ii) Stirling tail decay, and (iii) remainder absorptionunder Helson–Szegő factorization. Numerical verification on σ ∈ [0.58, 0.76] confirms a uniformpositive lower bound, offering an operator-theoretic path consistent with the Riemann Hypothesis.
Zeta function, Explicit formula, Báez–Duarte, Nyman–Beurling, Functional equation, Weighted least squares, Nyman–Beurling criterion, Number theory, Möbius function, Riemann, Zero-free region, Hilbert kernel, Analytic number theory, Numerical analysis
Zeta function, Explicit formula, Báez–Duarte, Nyman–Beurling, Functional equation, Weighted least squares, Nyman–Beurling criterion, Number theory, Möbius function, Riemann, Zero-free region, Hilbert kernel, Analytic number theory, Numerical analysis
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