Towards multiple elliptic polylogarithms
| dc.creator | Levin, Andrey | |
| dc.creator | Racinet, Georges | |
| dc.date | 2007-03-08 | |
| dc.date.accessioned | 2026-07-07T07:50:53Z | |
| dc.date.available | 2026-07-07T07:50:53Z | |
| dc.description | We investigate the elliptic analogs of multi-indexed polylogarithms that appear in the theory of the fundamental group of the projective line minus three points as sections of a universal nilpotent bundle with regular singular connection. We use an analytic uniformisation to derive the fundamental nilpotent De Rham torsor of a single elliptic curve in terms of a double Jacobi form introduced by Kronecker. We then extend this result to any smooth family, relatively to the base, i.e., to the moduli stack $M_{1,2}$ over $M_{1,1}$. Everything relies on explicit formulas that turn out to be algebraic for rational (families of) elliptic curves, and we conclude by providing the corresponding natural $\QM$ structure. | |
| dc.identifier | https://arxiv.org/abs/math/0703237 | |
| dc.identifier | http://arxiv.org/abs/math/0703237 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125319 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G55; 14H52; 33E05 | |
| dc.title | Towards multiple elliptic polylogarithms | |
| dc.type | text |