2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75507V. 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.Number Theory11M26text