The Critical Strips of the Sums 1 + 2z + ... + nz

We give a partition of the critical strip, associated with each partial sum 1 + 2z + ... + nz of the Riemann zeta function for Re z < −1, formed by infinitely many rectangles for which a formula allows us to count the number of its zeros inside each of them with an error, at most, of two zeros. A generalization of this formula is also given to a large class of almost-periodic functions with bounded spectrum.

A note on the real projection of the zeros of partial sums of Riemann zeta function

This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.