The Critical Strips of the Sums 1+2𝑧+⋯+𝑛𝑧
We give a partition of the critical strip, associated with each partial sum 1+2𝑧+⋯+𝑛𝑧 of the Riemann zeta function for 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 generaliz...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/909674 |
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| _version_ | 1849406494199513088 |
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| author | G. Mora J. M. Sepulcre |
| author_facet | G. Mora J. M. Sepulcre |
| author_sort | G. Mora |
| collection | DOAJ |
| description | We give a partition of the critical strip, associated with each partial sum 1+2𝑧+⋯+𝑛𝑧 of the Riemann zeta function for 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. |
| format | Article |
| id | doaj-art-4d96b90eab904bb5b4857a22cce5545b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4d96b90eab904bb5b4857a22cce5545b2025-08-20T03:36:22ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/909674909674The Critical Strips of the Sums 1+2𝑧+⋯+𝑛𝑧G. Mora0J. M. Sepulcre1Department of Mathematical Analysis, University of Alicante, 03080 Alicante, SpainDepartment of Mathematical Analysis, University of Alicante, 03080 Alicante, SpainWe give a partition of the critical strip, associated with each partial sum 1+2𝑧+⋯+𝑛𝑧 of the Riemann zeta function for 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.http://dx.doi.org/10.1155/2011/909674 |
| spellingShingle | G. Mora J. M. Sepulcre The Critical Strips of the Sums 1+2𝑧+⋯+𝑛𝑧 Abstract and Applied Analysis |
| title | The Critical Strips of the Sums 1+2𝑧+⋯+𝑛𝑧 |
| title_full | The Critical Strips of the Sums 1+2𝑧+⋯+𝑛𝑧 |
| title_fullStr | The Critical Strips of the Sums 1+2𝑧+⋯+𝑛𝑧 |
| title_full_unstemmed | The Critical Strips of the Sums 1+2𝑧+⋯+𝑛𝑧 |
| title_short | The Critical Strips of the Sums 1+2𝑧+⋯+𝑛𝑧 |
| title_sort | critical strips of the sums 1 2𝑧 ⋯ 𝑛𝑧 |
| url | http://dx.doi.org/10.1155/2011/909674 |
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