# Explicit formulas for Grassmannian polylogarithms

@article{Charlton2019ExplicitFF, title={Explicit formulas for Grassmannian polylogarithms}, author={Steven Charlton and Herbert Gangl and Danylo V. Radchenko}, journal={arXiv: Number Theory}, year={2019} }

We give a new explicit formula for Grassmannian polylogarithms in terms of iterated integrals. We also explicitly reduce the Grassmannian polylogarithm in weight 4 and in weight 5 each to depth 2. Furthermore, using this reduction in weight 4 we obtain an explicit, albeit complicated, form of the so-called 4-ratio, which gives an expression for the Borel class in continuous cohomology of $\mathrm{GL}_4$ in terms of $\mathrm{Li}_4$.

## 2 Citations

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We prove a conjecture of Goncharov, which says that any multiple polylogarithm can be expressed via polylogarithms of depth at most half of the weight. We give an explicit formula for this…

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