Plot zeros of partial sum of zeta Riemann with Maple

Question

I want to plot the zeros of the partial sum of the Riemann zeta function with Maple. Some hint??

Thanks!!!

Answer 1

Well, you could explore around to see where the zeroes might be via

partialZeta := proc(z, n) add(i^(-z),i=1..n) end;
ex1 := partialZeta(z, 20);
plots[complexplot3d](ex1, z=0-10*I..1+10*I, view=-1..4, axes=normal,grid=[500,500],scaling=constrained);

You will need to zoom in to see the zeroes. You can also use

fsolve(ex1, z, complex);

Probably even more useful is the RootFinding package, in particular RootFinding:-Analytic.