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

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

1999-10-11

arxiv.org/abs/math/9910055v3

Algebraic Methods in Probability and Statistics, Viana M. & Richards D. eds, Contemp. Math. 287, 23-26, American Mathematical

Mathematics

Number Theory

4 pages

Scientific paper

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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