Geodesic
Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic
Documenta mathematica, Tome 25 (2020), pp. 2355-2411.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Pellarin introduced the deformation of multiple zeta values of Thakur as elements over Tate algebras. In this paper, we relate these values to a certain coordinate of the logarithm of a higher dimensional Drinfeld module over the Tate algebra which we will introduce. Moreover, we define multiple polylogarithms in our setting and represent deformation of multiple zeta values as a linear combination of multiple polylogarithms. As an application of our results, we also write Dirichlet-Goss multiple $L$-values as a linear combination of twisted multiple polylogarithms at algebraic points.
Classification : 11R59, 11M38, 11M32
Keywords: multiple zeta values, Carlitz module, Tate algebras 
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     author = {Gezmi\c{s}, O\u{g}uz},
     title = {Deformation of {Multiple} {Zeta} {Values} and {Their} {Logarithmic} {Interpretation} in {Positive} {Characteristic}},
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Gezmiş, Oğuz. Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic. Documenta mathematica, Tome 25 (2020), pp. 2355-2411. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a6/