Hyper-Mahler measures via Goncharov-Deligne cyclotomy
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915267864428544 |
|---|---|
| author | Zhou, Yajun |
| author_facet | Zhou, Yajun |
| contents | The hyper-Mahler measures $m_k( 1+x_1+x_2),k\in\mathbb Z_{>1}$ and $m_k( 1+x_1+x_2+x_3),k\in\mathbb Z_{>1}$ are evaluated in closed form via Goncharov-Deligne periods, namely $\mathbb Q$-linear combinations of multiple polylogarithms at cyclotomic points (complex-valued coordinates that are roots of unity). Some infinite series related to these hyper-Mahler measures are also explicitly represented as Goncharov-Deligne periods of levels $1$, $2$, $ 3$, $4$, $6$, $8$, $10$ and $12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17243 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hyper-Mahler measures via Goncharov-Deligne cyclotomy Zhou, Yajun Number Theory High Energy Physics - Theory Combinatorics 11G55, 11M32, 11R06 The hyper-Mahler measures $m_k( 1+x_1+x_2),k\in\mathbb Z_{>1}$ and $m_k( 1+x_1+x_2+x_3),k\in\mathbb Z_{>1}$ are evaluated in closed form via Goncharov-Deligne periods, namely $\mathbb Q$-linear combinations of multiple polylogarithms at cyclotomic points (complex-valued coordinates that are roots of unity). Some infinite series related to these hyper-Mahler measures are also explicitly represented as Goncharov-Deligne periods of levels $1$, $2$, $ 3$, $4$, $6$, $8$, $10$ and $12$. |
| title | Hyper-Mahler measures via Goncharov-Deligne cyclotomy |
| topic | Number Theory High Energy Physics - Theory Combinatorics 11G55, 11M32, 11R06 |
| url | https://arxiv.org/abs/2210.17243 |