## Abstract and Applied Analysis

### The Critical Strips of the Sums $1 + 2 z + ⋯ + n z$

#### Abstract

We give a partition of the critical strip, associated with each partial sum $1+{2}^{z}+\cdots +{n}^{z}$ of the Riemann zeta function for Re $z\lt -1$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 909674, 15 pages.

Dates
First available in Project Euclid: 12 August 2011

https://projecteuclid.org/euclid.aaa/1313171152

Digital Object Identifier
doi:10.1155/2011/909674

Mathematical Reviews number (MathSciNet)
MR2793789

Zentralblatt MATH identifier
1213.30002

#### Citation

Mora, G.; Sepulcre, J. M. The Critical Strips of the Sums 1 + 2 z + ⋯ + n z. Abstr. Appl. Anal. 2011 (2011), Article ID 909674, 15 pages. doi:10.1155/2011/909674. https://projecteuclid.org/euclid.aaa/1313171152