## Euler-MacLaurin computation of zeta

Using PARI/gp, this past February:

We have a lower time of computation of 14 hours 26 min

when, in the notation of H.M. Edwards’ in his book,

N = 32,000 and ‘nu’ = 32,405 :

? N

%682 = 32000

? khyber

%683 = 32405

? t=0; q=s/(2*N*exp(s*log(N))); for(X=1,khyber,t=t+bernfrac(2*X)*q;\

q = q*((s+2*X-1)*(s+2*X)/(N*N))/((2*X+1)*(2*X+2)) );\

t = t + exp((1-s)*log(N))/(s-1) + exp(-s*log(N))/2 ; \

g = sum(X=1,N-1,exp(-s*log(X))); z2 = t+g; abs(z2)

%684 = 2.777212228894781921 E-60007

time = 14h, 25min, 44,279 ms.

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Mon Feb 18 06:38:42 EST 2013

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