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Differential and Functional Identities for the Elliptic Trilogarithm
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Differential and Functional Identities for the Elliptic Trilogarithm
Інший ID:
2000 Mathematics Subject Classification: 11F55; 53B50; 53D45
Посилання:
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.
Підтримка:
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.
Дата:
2009
Переглядів:
352
Завантажень:
211
Анотація:
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.
