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A general strong Nyman-Beurling Criterion for the Riemann Hypothesis | | Luis Baez-Duarte
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22 May 2005 | | Subject: | Number Theory | math.NT | | Abstract: | For each $f:[0,infty) oCom$ formally consider its co-Poisson or Müntz transform $g(x)=sum_{ngeq 1}f(nx)-frac{1}{x}int_0^infty f(t)dt$. For certain $f$’s with both $f, g in L_2(0,infty)$ it is true that the Riemann hypothesis holds if and only if $f$ is in the $L_2$ closure of the vector space generated by the dilations $g(kx)$, $kinNat$. Such is the case for example when $f=chi_{(0,1]}$ where the above statement reduces to the strong Nyman criterion already established by the author. In this note we show that the necessity implication holds for any continuously differentiable function $f$ vanishing at infinity and satisfying $int_0^infty t|f’(t)|dt | | Source: | arXiv, math.NT/0505453 | | Services: | Forum | Review | PDF | Favorites | |
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