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A note on Nyman's equivalent formulation of the Riemann Hypothesis

Jean-Francois Burnol
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Abstract

A certain subspace of the Hilbert space of square-integrable functions on the unit interval has been considered by Nyman, Beurling, and others, with the result that the constant function 1 belongs to it if and only if the Riemann Hypothesis holds. I show that the product of |1 - 1/rho| taken over the zeros with real parts strictly greater than 1/2, counted with multiplicities, is the norm of the projection of 1 to this subspace. This provides a quantitative refinement to Nyman's theorem.

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Jean-Francois Burnol. 2001-01-11. A note on Nyman's equivalent formulation of the Riemann Hypothesis. https://arxiv.org/abs/math/9910055

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