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- W2778351642 abstract "This work is a study of $p$-adic multiple zeta values at roots of unity ($p$MZV$mu_{N}$'s), the $p$-adic periods of the crystalline pro-unipotent fundamental groupoid of $(mathbb{P}^{1} - {0,mu_{N},infty})/ mathbb{F}_{q}$. The main tool is new objects which we call $p$-adic pro-unipotent harmonic actions. In this part IV we define and study $p$-adic analogues of some elementary complex analytic functions which interpolate multiple zeta values at roots of unity such as the multiple zeta functions. The indices of $p$MZV$mu_{N}$'s involve sequences of positive integers ; in this IV-1, by considering an operation which we call localization (inverting certain integration operators) in the pro-unipotent fundamental groupoid of $mathbb{P}^{1} - {0,mu_{N},infty}$, and by using $p$-adic pro-unipotent harmonic actions, we extend the definition of $p$MZV$mu_{N}$'s to indices for which these integers can be negative, and we study these generalized $p$MZV$mu_{N}$'s." @default.
- W2778351642 created "2018-01-05" @default.
- W2778351642 creator A5036185502 @default.
- W2778351642 date "2017-12-28" @default.
- W2778351642 modified "2023-09-27" @default.
- W2778351642 title "$p$-adic multiple zeta values at roots of unity and $p$-adic pro-unipotent harmonic actions - IV-1 : $p$-adic multiple zeta values at roots of unity extended to sequences of integers of any sign" @default.
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