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

Abstract EN

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.