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arXiv · 2503.23286

Diophantine approximation of multiple zeta-star values

Jiangtao Li
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Abstract

The set of multiple zeta-star values is a countable dense subset of the half line $(1,+\infty)$. In this paper, we establish some classical Diophantine type results for the set of multiple zeta-star values. Firstly, we give a criterion to determine whether a number is a multiple zeta-star value. Secondly, we establish the zero-one law for the set of multiple zeta-star value. Lastly, we propose a conjecture for the set of multiple zeta-star values, which strengthens the original zero-one law.

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Jiangtao Li. 2025-03-30. Diophantine approximation of multiple zeta-star values. https://arxiv.org/abs/2503.23286

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