An Approach to the Riemann Hypothesis using the Baez-Duarte Criterion and the Sylvester Sequence

This paper suggests an approach of the Riemann Hypothesis by satisfying theBaez-Duarte criterion. We construct an explicit approximation of the constantfunction 1 in the Hilbert space L2(0, 1) by choosing the coefficients ck to be identicalto the terms of the Sylvester sequence. The proof demonstrates that the infimum ofthe error vanishes, supported by the non-vanishing property of the Mellin multiplierand the convergence of the quadratic variation of discontinuities.