The critical strips of the sums \(1+2^{z}+\cdots +n^{z}\)
Summary: We give a partition of the critical strip, associated with each partial sum \(1 + 2^z + \dots + n^z\) of the Riemann zeta function for \(\text{Re\,}z < - 1\), 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.
partial sums of the Riemann zeta function
scientific article; zbMATH DE number 5888157