Geodesic
Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic
Documenta mathematica, Tome 25 (2020), pp. 2355-2411
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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.
DOI : 10.4171/dm/801
Classification : 11M32, 11M38, 11R59
Mots-clés : multiple zeta values, Carlitz module, Tate algebras 
@article{10_4171_dm_801,
     author = {O\u{g}uz Gezmi\c{s}},
     title = {Deformation of {Multiple} {Zeta} {Values} and {Their} {Logarithmic} {Interpretation} in {Positive} {Characteristic}},
     journal = {Documenta mathematica},
     pages = {2355--2411},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/801},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/801/}
}
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Oğuz Gezmiş. Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic. Documenta mathematica, Tome 25 (2020), pp. 2355-2411. doi: 10.4171/dm/801

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