Simple and accurate approximations to the Riemann zeta function
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917518404222976 |
|---|---|
| author | Kuznetsov, Alexey |
| author_facet | Kuznetsov, Alexey |
| contents | We develop approximations for the Riemann zeta function that enable high-precision computation within the critical strip and other vertical strips. These approximations combine the main sum of the Riemann-Siegel formula with a simple approximation of the remainder term, which involves only elementary functions and certain precomputed coefficients obtained via Gaussian quadrature. Additionally, we provide approximations for the derivative of the Riemann zeta function and present extensive numerical evidence demonstrating the accuracy of these approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple and accurate approximations to the Riemann zeta function Kuznetsov, Alexey Number Theory Numerical Analysis Primary 11M06, Secondary 11Y35 We develop approximations for the Riemann zeta function that enable high-precision computation within the critical strip and other vertical strips. These approximations combine the main sum of the Riemann-Siegel formula with a simple approximation of the remainder term, which involves only elementary functions and certain precomputed coefficients obtained via Gaussian quadrature. Additionally, we provide approximations for the derivative of the Riemann zeta function and present extensive numerical evidence demonstrating the accuracy of these approximations. |
| title | Simple and accurate approximations to the Riemann zeta function |
| topic | Number Theory Numerical Analysis Primary 11M06, Secondary 11Y35 |
| url | https://arxiv.org/abs/2503.09519 |