Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve
This paper draws connections between the double shuffle equations and structure of associators; universal mixed elliptic motives as defined by Hain and Matsumoto; and the Rankin-Selberg method for modular forms for $SL_2(\mathbb{Z})$. We write down explicit formulae for zeta elements $\sigma_{2n-1}$...
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| 格式: | Journal article |
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Cambridge University Press
2017
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| _version_ | 1826268455106510848 |
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| author | Brown, F |
| author_facet | Brown, F |
| author_sort | Brown, F |
| collection | OXFORD |
| description | This paper draws connections between the double shuffle equations and structure of associators; universal mixed elliptic motives as defined by Hain and Matsumoto; and the Rankin-Selberg method for modular forms for $SL_2(\mathbb{Z})$. We write down explicit formulae for zeta elements $\sigma_{2n-1}$ (generators of the Tannaka Lie algebra of the category of mixed Tate motives over $\mathbb{Z}$) in depths up to four, give applications to the Broadhurst-Kreimer conjecture, and completely solve the double shuffle equations for multiple zeta values in depths two and three |
| first_indexed | 2024-03-06T21:09:55Z |
| format | Journal article |
| id | oxford-uuid:3dc9c8fb-8a5b-46b4-afe9-147e691733ed |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:09:55Z |
| publishDate | 2017 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:3dc9c8fb-8a5b-46b4-afe9-147e691733ed2022-03-26T14:21:32ZZeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curveJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3dc9c8fb-8a5b-46b4-afe9-147e691733edSymplectic Elements at OxfordCambridge University Press2017Brown, FThis paper draws connections between the double shuffle equations and structure of associators; universal mixed elliptic motives as defined by Hain and Matsumoto; and the Rankin-Selberg method for modular forms for $SL_2(\mathbb{Z})$. We write down explicit formulae for zeta elements $\sigma_{2n-1}$ (generators of the Tannaka Lie algebra of the category of mixed Tate motives over $\mathbb{Z}$) in depths up to four, give applications to the Broadhurst-Kreimer conjecture, and completely solve the double shuffle equations for multiple zeta values in depths two and three |
| spellingShingle | Brown, F Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve |
| title | Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve |
| title_full | Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve |
| title_fullStr | Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve |
| title_full_unstemmed | Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve |
| title_short | Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve |
| title_sort | zeta elements in depth 3 and the fundamental lie algebra of the infinitesimal tate curve |
| work_keys_str_mv | AT brownf zetaelementsindepth3andthefundamentalliealgebraoftheinfinitesimaltatecurve |