The message below was sent to the old Arizona math-fun list. (The first non-spam message in months.) Mr Agol is not a Math-Fun subscriber, so CC him on any comments. Rich rcs@cs.arizona.edu ---------------------- Date: Wed, 21 Jan 2004 23:53:43 -0600 (CST) From: Ian Agol <agol@math.uic.edu> To: math-fun@CS.Arizona.EDU Subject: conjecture => RH If one writes: 1/Zeta[1/(1-z)]= Sum a_n z^n, then RH is equivalent to limsup |a_n|^(1/n) = 1. Computing a_n with mathematica, it seems that |a_n|<1, and oscillates between +-.02 to n=900. It seems reasonable to conjecture that a_n -> 0. Does anyone know if this conjecture has been made before, or if it is implied by some stronger published conjecture? Can anyone compute more terms of this series to see if it holds up? Using known bounds on the Stieltjes constants, I can numerically show that the radius of convergence of the series is at least .56. Can anyone improve on this? thanks, Ian Agol