Note on the number of zeros of $$\zeta ^{(k)}(s)$$
| Autor: | Fan Ge, Ade Irma Suriajaya |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Mathematics - Number Theory Mathematics::Number Theory 010102 general mathematics Zero (complex analysis) 0102 computer and information sciences Derivative 01 natural sciences Combinatorics symbols.namesake Riemann hypothesis 11M06 Number theory 010201 computation theory & mathematics Fourier analysis symbols Pi 0101 mathematics Mathematics |
| Zdroj: | The Ramanujan Journal. 55:661-672 |
| ISSN: | 1572-9303 1382-4090 |
| DOI: | 10.1007/s11139-019-00219-z |
| Popis: | Assuming the Riemann hypothesis, we prove that $$ N_k(T) = \frac{T}{2\pi}\log \frac{T}{4\pi e} + O_k\left(\frac{\log{T}}{\log\log{T}}\right), $$ where $N_k(T)$ is the number of zeros of $\zeta^{(k)}(s)$ in the region $0 Comment: 10 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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