On the approximation of the zeta function by Dirichlet polynomials
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917703472644096 |
|---|---|
| author | de Reyna, Juan Arias |
| author_facet | de Reyna, Juan Arias |
| contents | We prove that for $s=σ+it$ with $σ\ge0$ and $0<t\le x$, we have \[ζ(s)=\sum_{n\le x}n^{-s}+\frac{x^{1-s}}{(s-1)}+Θ\frac{29}{14} x^{-σ},\qquad \frac{29}{14}=2.07142\dots\] where $Θ$ is a complex number with $|Θ|\le1$. This improves Theorem 4.11 of Titchmarsh. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the approximation of the zeta function by Dirichlet polynomials de Reyna, Juan Arias Number Theory Primary 11M06, Secondary 30D99 We prove that for $s=σ+it$ with $σ\ge0$ and $0<t\le x$, we have \[ζ(s)=\sum_{n\le x}n^{-s}+\frac{x^{1-s}}{(s-1)}+Θ\frac{29}{14} x^{-σ},\qquad \frac{29}{14}=2.07142\dots\] where $Θ$ is a complex number with $|Θ|\le1$. This improves Theorem 4.11 of Titchmarsh. |
| title | On the approximation of the zeta function by Dirichlet polynomials |
| topic | Number Theory Primary 11M06, Secondary 30D99 |
| url | https://arxiv.org/abs/2406.16667 |