Does anybody know what is the order of the remainder (rest) of the Dirichlet sum (which has for limit Zeta(s) for s in between 0 and 1 not included)?
I mean, is there an equivalent of the rest, as for instance in N^s or N^(1-s) for big N, where N would be the last term in the sum? I tried to estimate it I think it should be either N^s or N^(1-s) depending on which one is bigger, but I am really not sure. Is that correct? Perhaps there is simply no way to find an order of the equivalent ?. If there is does anybody have a link where I could read about it?


PS: sorry I do not know yet how to use the mathematical symbols here , but I will learn!