A divergent Vasyunin correction

Details A divergent Vasyunin correction A divergent Vasyunin correction

2005-06-16

arxiv.org/abs/math/0506318v1

Mathematics

Number Theory

Scientific paper

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.

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