Evidence in Favor of the Baez-Duarte Criterion for the Riemann Hypothesis

We present the results of the numerical experiments in favor of the Baez-Duarte criterion for the Riemann Hypothesis. We give formulae allowing calculation of numerical values of the numbers ck appearing in this criterion for arbitrary large k. We present plots of ck for ( ) 9 1, 10 . k ∈

[1]  Cheng-Nan Lai,et al.  Two conditions for reducing the maximal length of node-disjoint paths in hypercubes , 2012, Theor. Comput. Sci..

[2]  M. Wolf,et al.  Criteria equivalent to the Riemann Hypothesis , 2008, 0808.0640.

[3]  M. Coffey.  On the coefficients of the Baez-Duarte criterion for the Riemann hypothesis and their extensions , 2006, math-ph/0608050.

[4]  S. Beltraminelli,et al.  Riemann Hypothesis: The Riesz-Hardy-Littlewood wave in the long wavelength region , 2006, math/0605565.

[5]  S. Beltraminelli,et al.  The criteria of Riesz, Hardy-Littlewood et al. for the Riemann Hypothesis revisited using similar functions , 2006, math/0601138.

[6]  L. Báez-Duarte.  A new necessary and sufficient condition for the Riemann hypothesis , 2003, math/0307215.

[7]  K. Mašlanka.  Hypergeometric-like Representation of the Zeta-Function of Riemann , 2001, math-ph/0105007.

[8]  Andrew M. Odlyzko,et al.  An improved bound for the de Bruijn–Newman constant , 2000, Numerical Algorithms.

[9]  J. Pitman,et al.  Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions , 1999, math/9912170.

[10]  Xian-jin Li,et al.  The Positivity of a Sequence of Numbers and the Riemann Hypothesis , 1997 .

[11]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[12]  D. R. Heath-Brown,et al.  The Theory of the Riemann Zeta-Function , 1987 .

[13]  C. Ogilvy.  The Binomial Coefficients , 1950 .

[14]  M. Riesz.  Sur l’hypothèse de Riemann , 1916 .

[15]  W. Burnside.  Theory of Functions , 1899, Nature.

[16]  Luis Báez-Duarte,et al.  A sequential Riesz-like criterion for the Riemann hypothesis , 2005, Int. J. Math. Math. Sci..

[17]  Luis Báez-Duarte,et al.  Möbius convolutions and the Riemann hypothesis , 2005, Int. J. Math. Math. Sci..

[18]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science (2. ed.) , 1994 .

[19]  R. C. Baker,et al.  THE THEORY OF THE RIEMANN ZETA‐FUNCTION (2nd edition) (Oxford Science Publications) , 1988 .