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arXiv · 1701.05729

Cyclotomic p-adic multi-zeta values

Sinan Unver
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Abstract

The cyclotomic $p$-adic multi-zeta values are the $p$-adic periods of $π_{1}(\mathbb{G}_{m} \setminus μ_{M},\cdot),$ 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.

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Sinan Unver. 2017-01-20. Cyclotomic p-adic multi-zeta values. https://arxiv.org/abs/1701.05729

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