Tau and Lambda graphics

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 [Graphics:Images/index_gr_1.gif] and [Graphics:Images/index_gr_2.gif](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_3.gif]

[Graphics:Images/index_gr_4.gif]

[Graphics:Images/index_gr_5.gif]

[Graphics:Images/index_gr_6.gif]

Computed by Rick Kreminski    November 2003


Converted by Mathematica      August 10, 2004