is it just me? I find it confusing when it is claimed that "all non-trivial zero's of Zeta[x+I y] lie 'on' the line x=1/2 " (* original claim *) since much more seems to be happening. Is that because of my lack of understanding the shorthand used? I would say three things instead: 1/ only for x=1/2 does the function Zeta[x+ I y] pass through *one single intersection point* for each revolution of its modulus [0 , 2Pi] 2/ and for x=1/2 that special point also 'magically' happens to be {0,0} 3/ apart from x=1/2, Zeta[x+ I y] always 'magically' misses the point {0,0} (* equivalent to original claim *) ... and, if x>1/2, it crosses y=0 somehere Re[ it ] >0, and if x<1/2, then at Re[ it ] <0. Everytime. Ha! The original formulation leaves it open whether Zeta[1/2+ I y] could ever *not* pass through {0,0} during a complete turn of its modulus (passing somehere through {u, 0} with u < 0.1 say, like between y= 110 and 112) But, maybe my concept of "revolution around a center from where its modulus is seen to monotonously increase" is completely naive. Can such thing be defined for good old Zeta? Would { 0+epsilon, 0 } do? hmmmppfff (puffing...). Why don't people simply say such things up front? Wouter.