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A strengthening of the Nyman-Beurling criterion for the Riemann Hypothesis | Luis Baez-Duarte
; | Date: |
15 Feb 2002 | Subject: | Number Theory | math.NT | Abstract: | Let $
ho(x)=x-[x]$, $chi=chi_{(0,1)}$. In $L_2(0,infty)$ consider the subspace $B$ generated by ${
ho_a | a geq 1}$ where $
ho_a(x):=
ho(frac{1}{ax})$. By the Nyman-Beurling criterion the Riemann hypothesis is equivalent to the statement $chiinar{B}$. For some time it has been conjectured, and proved in this paper, that the Riemann hypothesis is equivalent to the stronger statement that $chiinar{Bnat}$ where $Bnat$ is the much smaller subspace generated by ${
ho_a | ainNat}$. | Source: | arXiv, math.NT/0202141 | Services: | Forum | Review | PDF | Favorites |
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