On the lower bounds of the partial sums of a Dirichlet series
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Title: | On the lower bounds of the partial sums of a Dirichlet series |
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Authors: | Mora, Gaspar | Benítez, Edgar |
Research Group/s: | Curvas Alpha-Densas. Análisis y Geometría Local |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Dirichlet series | Zeros of partial sums of Dirichlet series | Henry lower bound |
Knowledge Area: | Análisis Matemático |
Issue Date: | 15-Apr-2022 |
Publisher: | Springer Nature |
Citation: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2022, 116:97. https://doi.org/10.1007/s13398-022-01237-1 |
Abstract: | In this paper it is shown that for the ordinary Dirichlet series, ∑∞j=0αj(j+1)s, α0=1, of a class, say P, that contains in particular the series that define the Riemann zeta and the Dirichlet eta functions, there exists limn→∞ρn/n, where the ρn’s are the Henry lower bounds of the partial sums of the given Dirichlet series, Pn(s)=∑n−1j=0αj(j+1)s, n>2. Likewise it is given an estimate of the above limit. For the series of P having positive coefficients it is shown the existence of the limn→∞aPn(s)/n, where the aPn(s)’s are the lowest bounds of the real parts of the zeros of the partial sums. Furthermore it has been proved that limn→∞aPn(s)/n=limn→∞ρn/n. |
Sponsor: | Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. |
URI: | http://hdl.handle.net/10045/123144 |
ISSN: | 1578-7303 (Print) | 1579-1505 (Online) |
DOI: | 10.1007/s13398-022-01237-1 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Peer Review: | si |
Publisher version: | https://doi.org/10.1007/s13398-022-01237-1 |
Appears in Collections: | INV - CADAGL - Artículos de Revistas |
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Mora_Benitez_2022_RevRealAcadCiencExactasFisNatSerAMat.pdf | 305,14 kB | Adobe PDF | Open Preview | |
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