Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2309.07569 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908666057195520 |
|---|---|
| author | Li, Jiangtao |
| author_facet | Li, Jiangtao |
| contents | We provide a multiple integral representation for each multiple zeta-star value, and utilize these representations to establish a natural order structure on the set of such values. This order structure allows for a one-to-one correspondence between a subset of the infinite sequences of natural numbers and the half line $(1,+\infty)$. Some basic properties of this correspondence are discussed. We also calculate the Hausdorff dimensions for the images of some subsets of the infinite sequences under this correspondence. As a result of this correspondence, we are able to determine the limits for a number of natural multiple integrals. Our analysis also reveals that the set of multiple zeta-star values is dense within the $(1,+\infty)$ domain, and that each value is non-integer in nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07569 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The topology of the set of multiple zeta-star values Li, Jiangtao Number Theory We provide a multiple integral representation for each multiple zeta-star value, and utilize these representations to establish a natural order structure on the set of such values. This order structure allows for a one-to-one correspondence between a subset of the infinite sequences of natural numbers and the half line $(1,+\infty)$. Some basic properties of this correspondence are discussed. We also calculate the Hausdorff dimensions for the images of some subsets of the infinite sequences under this correspondence. As a result of this correspondence, we are able to determine the limits for a number of natural multiple integrals. Our analysis also reveals that the set of multiple zeta-star values is dense within the $(1,+\infty)$ domain, and that each value is non-integer in nature. |
| title | The topology of the set of multiple zeta-star values |
| topic | Number Theory |
| url | https://arxiv.org/abs/2309.07569 |