I'm trying to understand how the zeros of the zeta function can be

used to approximate pi(x).

From Tomás Oliveira e Silva's webpage I understand that if we define

H(x)=2*(li(x)-pi(x))/pi(sqrt(x))

which can be thought of as way of displaying the normalised

irregularities in the distribution. It can be approximated by

H(x)=1+2*sum(sin(t*ln(x))/t) where t are the zeros of the zeta

function

I've plotted H(x) and its approximation using the zeroes for primes

up to 1000000 and the wiggly shape of both functions is the same but

there's an offset between the two graphs which is neither a constant

increment or a constant ratio.

Is this correct or am I missing something?

Perhaps if I could get hold of a copy of "Zeroes of Dirichlet L-

functions and irregularities in the distribution of primes" by Carter

Bays and Richard H. Hudson I could work out where I went wrong. Does

anyone have a copy?

Cheers!

Richard