Möbius convolutions and the Riemann hypothesis.
A sequential Riesz-like criterion for the Riemann Hypothesis.
On Maslanka's representation for the Riemann zeta function.
New versions of the Nyman-Beurling criterion for the Riemann hypothesis.
A strengthening of the Nyman-Beurling criterion for the Riemann hypothesis
According to the well-known Nyman-Beurling criterion the Riemann hypothesis is equivalent to the possibility of approximating the characteristic function of the interval in mean square norm by linear combinations of the dilations of the fractional parts for real greater than . It was conjectured and established here that the statement remains true if the dilations are restricted to those where the ’s are positive integers. A constructive sequence of such approximations is given.
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