The meta-abelian elliptic KZB associator and periods of Eisenstein series
We compute the image of Enriquez’ elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve.Our main result is an explicit formula for this image in terms of Eichler integrals of Eisenstein series, and is analogous to Deligne’s c...
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| Format: | Journal article |
| Language: | English |
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Springer
2017
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| _version_ | 1797063778720808960 |
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| author | Matthes, N |
| author_facet | Matthes, N |
| author_sort | Matthes, N |
| collection | OXFORD |
| description | We compute the image of Enriquez’ elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve.Our main result is an explicit formula for this image in terms of Eichler integrals of Eisenstein series, and is analogous to Deligne’s computation of the depth one quotient of the Drinfeld associator.We also show how to retrieve Zagier’s extended period polynomials of Eisenstein series, as well as the values at zero of Beilinson–Levin’s elliptic polylogarithms from the meta-abelian elliptic KZB associator. |
| first_indexed | 2024-03-06T21:04:47Z |
| format | Journal article |
| id | oxford-uuid:3c147ccc-3858-4a0c-a163-dd39bd4e24f0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:04:47Z |
| publishDate | 2017 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:3c147ccc-3858-4a0c-a163-dd39bd4e24f02022-03-26T14:11:25ZThe meta-abelian elliptic KZB associator and periods of Eisenstein seriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3c147ccc-3858-4a0c-a163-dd39bd4e24f0EnglishSymplectic Elements at OxfordSpringer2017Matthes, NWe compute the image of Enriquez’ elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve.Our main result is an explicit formula for this image in terms of Eichler integrals of Eisenstein series, and is analogous to Deligne’s computation of the depth one quotient of the Drinfeld associator.We also show how to retrieve Zagier’s extended period polynomials of Eisenstein series, as well as the values at zero of Beilinson–Levin’s elliptic polylogarithms from the meta-abelian elliptic KZB associator. |
| spellingShingle | Matthes, N The meta-abelian elliptic KZB associator and periods of Eisenstein series |
| title | The meta-abelian elliptic KZB associator and periods of Eisenstein series |
| title_full | The meta-abelian elliptic KZB associator and periods of Eisenstein series |
| title_fullStr | The meta-abelian elliptic KZB associator and periods of Eisenstein series |
| title_full_unstemmed | The meta-abelian elliptic KZB associator and periods of Eisenstein series |
| title_short | The meta-abelian elliptic KZB associator and periods of Eisenstein series |
| title_sort | meta abelian elliptic kzb associator and periods of eisenstein series |
| work_keys_str_mv | AT matthesn themetaabelianelliptickzbassociatorandperiodsofeisensteinseries AT matthesn metaabelianelliptickzbassociatorandperiodsofeisensteinseries |