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A divergent Vasyunin correction | | Luis Baez-Duarte
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16 Jun 2005 | | Subject: | Number Theory MSC-class: 11M26 | math.NT | | Abstract: | V. I. Vasyunin has introduced special sequences of step functions related to the strong Nyman-Beurling criterion that converge pointwise to 1 in $[1,infty)$. We show here that the first and simplest such sequence considered by Vasyunin diverges in $L_1((1,infty),x^{-2}dx)$, which of course precludes the $L_2((1,infty),x^{-2}dx)$-convergence needed for the Riemann hypothesis. Whether all sequences considered by this author also diverge remains an interesting open question. | | Source: | arXiv, math.NT/0506318 | | Services: | Forum | Review | PDF | Favorites | |
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