On distribution formulas for complex and \(l\)-adic polylogarithms. (English) Zbl 1456.11121
Burgos Gil, José Ignacio (ed.) et al., Periods in quantum field theory and arithmetic. Based on the presentations at the research trimester on multiple zeta values, multiple polylogarithms, and quantum field theory, ICMAT 2014, Madrid, Spain, September 15–19, 2014. Cham: Springer. Springer Proc. Math. Stat. 314, 593-619 (2020).
Summary: We study an \(l\)-adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors. As a goal, we obtain a notion of certain universal Kummer-Heisenberg measures that enable interpolating the \(l\)-adic polylogarithmic distribution relations for all degrees.
For the entire collection see [Zbl 1446.81002].
For the entire collection see [Zbl 1446.81002].
MSC:
| 11G55 | Polylogarithms and relations with \(K\)-theory |
| 19F27 | Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) |
| 11R70 | \(K\)-theory of global fields |
| 19D45 | Higher symbols, Milnor \(K\)-theory |
Keywords:
arithmetic fundamental group; Galois actions on étale paths; functional equations of polylogarithmsReferences:
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