Elliptic double zeta values
We study an elliptic analogue of multiple zeta values, the elliptic multiple zeta values of Enriquez, which are the coefficients of the el liptic KZB associator. Originally defined by iterated integrals on a once-punctured complex elliptic curve, it turns out that they can also be expressed as certa...
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| Materiálatiipa: | Journal article |
| Giella: | English |
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Elsevier
2016
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| _version_ | 1826300357956861952 |
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| author | Matthes, N |
| author_facet | Matthes, N |
| author_sort | Matthes, N |
| collection | OXFORD |
| description | We study an elliptic analogue of multiple zeta values, the elliptic multiple zeta values of Enriquez, which are the coefficients of the el liptic KZB associator. Originally defined by iterated integrals on a once-punctured complex elliptic curve, it turns out that they can also be expressed as certain linear combinations of indefinite iterated integrals of Eisenstein series and multiple zeta values. In this paper, we prove that the Q-span of these elliptic multiple zeta values forms a Q-algebra, which is naturally filtered by the length and is conjecturally graded by the weight. Our main result is a proof of a formula for the number of Q-linearly independent elliptic multiple zeta values of lengths one and two for arbitrary weight. |
| first_indexed | 2024-03-07T05:15:55Z |
| format | Journal article |
| id | oxford-uuid:dd2b4250-5b29-48a7-a67f-3a9b11d5bfb4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:15:55Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:dd2b4250-5b29-48a7-a67f-3a9b11d5bfb42022-03-27T09:23:16ZElliptic double zeta valuesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dd2b4250-5b29-48a7-a67f-3a9b11d5bfb4EnglishSymplectic Elements at OxfordElsevier2016Matthes, NWe study an elliptic analogue of multiple zeta values, the elliptic multiple zeta values of Enriquez, which are the coefficients of the el liptic KZB associator. Originally defined by iterated integrals on a once-punctured complex elliptic curve, it turns out that they can also be expressed as certain linear combinations of indefinite iterated integrals of Eisenstein series and multiple zeta values. In this paper, we prove that the Q-span of these elliptic multiple zeta values forms a Q-algebra, which is naturally filtered by the length and is conjecturally graded by the weight. Our main result is a proof of a formula for the number of Q-linearly independent elliptic multiple zeta values of lengths one and two for arbitrary weight. |
| spellingShingle | Matthes, N Elliptic double zeta values |
| title | Elliptic double zeta values |
| title_full | Elliptic double zeta values |
| title_fullStr | Elliptic double zeta values |
| title_full_unstemmed | Elliptic double zeta values |
| title_short | Elliptic double zeta values |
| title_sort | elliptic double zeta values |
| work_keys_str_mv | AT matthesn ellipticdoublezetavalues |