A divergent Vasyunin correction

Original · EN

V. I. Vasyunin has introduced special sequences of step functions related to the strong Nyman-Beurling criterion that converge pointwise to 1 in [1,∞). We show here that the first and simplest such sequence considered by Vasyunin diverges in L₁((1,∞),x⁻²dx), which of course precludes the L₂((1,∞),x⁻²dx)-convergence needed for the Riemann hypothesis. Whether all sequences considered by this author also diverge remains an interesting open question.