c:=40

a:=1.35
t:=7
w:=a+t*I

zt1:=(Abs[Sum[1/k^w , {k,1,c}]])^2

zr2:=2*Sum[Sum[Cos[t*Log[(k-r)/k]]/(((k-r)^a)*(k^a)) , {r,0,k-1}] ,{k,0,c}]

zr3:=Sum[1/(k^(2*a)) , {k,1,c}]

result:=zr2-zr3

N[zt1,14]
N[result,14]

1.1847161348425
1.1847161348425

    Source: geocities.com/timeparadox