A strengthening of the Nyman-Beurling criterion for the Riemann Hypothesis

2002/02/15 by Luis Báez‐Duarte, Luis Baez-Duarte, Baez-Duarte, Luis · 5 citations
Mathematics · #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.NT

paper · pdf · doi:10.48550/arxiv.math/0202141

7 pages, 3 typos corrected, one reference added

arxiv created 2002/02/18 · arxiv updated 2009/11/30

Abstract

Let ρ(x)=x-[x], χ=χ_(0,1). In L₂(0,∞) consider the subspace \B generated by \ρ_a | a ≥ 1\ where ρ_a(x):=ρ((1)/(ax)). By the Nyman-Beurling criterion the Riemann hypothesis is equivalent to the statement χ∈\B. For some time it has been conjectured, and proved in this paper, that the Riemann hypothesis is equivalent to the stronger statement that χ∈\Bnat where \Bnat is the much smaller subspace generated by \ρ_a | a∈\Nat\.

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