A General Strong Nyman-beurling Criterion for the Riemann Hypothesis

  • Luis B, Aez-Duarte
  • Published 2005
For each f : [0, ∞) → C formally consider its co-Poisson or Müntz transform g(x) = n≥1 f (nx) − 1 x ∞ 0 f (t)dt. For certain f 's with both f, g ∈ L2(0, ∞) it is true that the Riemann hypothesis holds if and only if f is in the L2 closure of the vector space generated by the dilations g(kx), k ∈ N. Such is the case for example when f = χ (0,1] where the… CONTINUE READING