The Critical Strips of the Sums 1+2z+⋯+nz. (5th May 2011)

• Record Type: Journal Article
• Authors: Mora, G.; Sepulcre, J. M.
• Other Names: Clark Stephen Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2011(2011)
• Publication Date: 2011-05-05
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2011/909674
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We give a partition of the critical strip, associated with each partial sum1 + 2 z + ⋯ + n z of the Riemann zeta function for Rez < − 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.