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

Key Points

• The aim is to explore a new method to tackle the Riemann Hypothesis using the Baez-Duarte criterion.
• Constructing an approximation of the constant function 1 in Hilbert space L2(0, 1) using coefficients from the Sylvester sequence.
• Showing that the infimum of the error approaches zero.
• Using the properties of the Mellin multiplier to support the proof.
• Analyzing the convergence of the quadratic variation of discontinuities.
• The proof shows that the error vanishes as the approximation improves.
• The non-vanishing property of the Mellin multiplier assists in the approach's validity.