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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |