A strengthening of the Nyman-Beurling criterion for the Riemann Hypothesis
Luis Baez-Duarte
Abstract
Let ρ(x)=x-[x], χ=χ(0,1). In L2(0,∞) consider the subspace generated by \ρa | a ≥ 1\ where ρa(x):=ρ(1ax). By the Nyman-Beurling criterion the Riemann hypothesis is equivalent to the statement χ∈. For some time it has been conjectured, and proved in this paper, that the Riemann hypothesis is equivalent to the stronger statement that χ∈ where is the much smaller subspace generated by \ρa | a∈\.
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