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arXiv · 2508.18320

Shintani's invariant via cyclic quantum dilogarithm

Bora Yalkinoglu
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Abstract

We formulate Shintani's invariant in terms of the cyclic quantum dilogarithm. Building on earlier results that expressed Shintani's invariant using the $q$-Pochhammer symbol, we show how the cyclic quantum dilogarithm naturally arises in this context, providing new perspectives on the arithmetic significance of Shintani's construction. The present note is an announcement; a full account with complete proofs will appear in a forthcoming paper.

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Bora Yalkinoglu. 2025-08-24. Shintani's invariant via cyclic quantum dilogarithm. https://arxiv.org/abs/2508.18320

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