The Critical Strips of the Sums 1 + 2 𠑧 + ⋯ + 𠑛 𠑧

G. Mora and J. M. Sepulcre

Abstract and Applied Analysis, 2011, vol. 2011, 1-15

Abstract:

We give a partition of the critical strip, associated with each partial sum 1 + 2 𠑧 + ⋯ + 𠑛 𠑧 of the Riemann zeta function for Re 𠑧 < − 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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:909674

DOI: 10.1155/2011/909674

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