The Riemann hypothesis has several equivalent forms, as described by J. Keiper in "Power series expansions of Riemann's ζ function" Mathematics of Computation, 1992 (p765-773). Both
and
(denoted lamda(k) and tau(k)) are coefficients of power series having the property that their radius of convergence is 1 iff the Riemann hypothesis holds true. Below is some numerical evidence for the RH, where lambda(k) and tau(k) are computed from our computations of the Stieltjes constants
![[Graphics:Images/index_gr_4.gif]](Images/index_gr_4.gif)
![[Graphics:Images/index_gr_5.gif]](Images/index_gr_5.gif)
![[Graphics:Images/index_gr_6.gif]](Images/index_gr_6.gif)
Computed by Rick Kreminski November 2003