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# Title: Cyclotomic p-adic multi-zeta values

Authors: Sinan Unver
Abstract: The cyclotomic $p$-adic multi-zeta values are the $p$-adic periods of $\pi_{1}(\mathbb{G}_{m} \setminus \mu_{M},\cdot),$ the unipotent fundamental group of the multiplicative group minus the $M$-th roots of unity. In this paper, we compute the cyclotomic $p$-adic multi-zeta values at all depths. This paper generalizes the results in [6] and [7]. Since the main result gives explicit formulas we expect it to be useful in proving non-vanishing and transcendence results for these $p$-adic periods and also, through the use of $p$-adic Hodge theory, in proving non-triviality results for the corresponding $p$-adic Galois representations.
 Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG) Cite as: arXiv:1701.05729 [math.NT] (or arXiv:1701.05729v1 [math.NT] for this version)

## Submission history

From: Sinan Unver [view email]
[v1] Fri, 20 Jan 2017 09:10:49 GMT (13kb)
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