Differential and Functional Identities for the Elliptic Trilogarithm
When written in terms of J-functions, the classical Frobenius-Stickelberger pseudo-addition formula takes a very simple form. Generalizations of this functional identity are studied, where the functions involved are derivatives (including derivatives with respect to the modular parameter) of the ell...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149173 |
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| Cite this: | Differential and Functional Identities for the Elliptic Trilogarithm / Ian A.B. Strachan // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-149173 |
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Strachan, Ian A.B. 2019-02-19T18:02:02Z 2019-02-19T18:02:02Z 2009 Differential and Functional Identities for the Elliptic Trilogarithm / Ian A.B. Strachan // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 23 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 11F55; 53B50; 53D45 https://nasplib.isofts.kiev.ua/handle/123456789/149173 When written in terms of J-functions, the classical Frobenius-Stickelberger pseudo-addition formula takes a very simple form. Generalizations of this functional identity are studied, where the functions involved are derivatives (including derivatives with respect to the modular parameter) of the elliptic trilogarithm function introduced by Beilinson and Levin. A differential identity satisfied by this function is also derived. These generalized Frobenius-Stickelberger identities play a fundamental role in the development of elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde equations of associativity, with the simplest case reducing to the above mentioned differential identity. This paper is a contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21–25, 2008, MPIM, Bonn, Germany). I would like to thank Harry Braden, who first showed me that (2) was just the Frobenius–Stickelberger identity (1), and Misha Feigin and Andrew Riley for their comments and remarks. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Differential and Functional Identities for the Elliptic Trilogarithm Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Differential and Functional Identities for the Elliptic Trilogarithm |
| spellingShingle |
Differential and Functional Identities for the Elliptic Trilogarithm Strachan, Ian A.B. |
| title_short |
Differential and Functional Identities for the Elliptic Trilogarithm |
| title_full |
Differential and Functional Identities for the Elliptic Trilogarithm |
| title_fullStr |
Differential and Functional Identities for the Elliptic Trilogarithm |
| title_full_unstemmed |
Differential and Functional Identities for the Elliptic Trilogarithm |
| title_sort |
differential and functional identities for the elliptic trilogarithm |
| author |
Strachan, Ian A.B. |
| author_facet |
Strachan, Ian A.B. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
When written in terms of J-functions, the classical Frobenius-Stickelberger pseudo-addition formula takes a very simple form. Generalizations of this functional identity are studied, where the functions involved are derivatives (including derivatives with respect to the modular parameter) of the elliptic trilogarithm function introduced by Beilinson and Levin. A differential identity satisfied by this function is also derived. These generalized Frobenius-Stickelberger identities play a fundamental role in the development of elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde equations of associativity, with the simplest case reducing to the above mentioned differential identity.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149173 |
| citation_txt |
Differential and Functional Identities for the Elliptic Trilogarithm / Ian A.B. Strachan // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 23 назв. — англ. |
| work_keys_str_mv |
AT strachanianab differentialandfunctionalidentitiesfortheelliptictrilogarithm |
| first_indexed |
2025-12-07T18:56:53Z |
| last_indexed |
2025-12-07T18:56:53Z |
| _version_ |
1850876953160056832 |