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arXiv · 2411.06763

The Shintani--Faddeev modular cocycle: Stark units from $q$-Pochhammer ratios

Gene S. Kopp
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Abstract

We give a new interpretation of Stark units associated to real quadratic fields as real multiplication values of a modular cocycle. The cocycle of interest is a meromorphic factor describing the modular transformations of the $q$-Pochhammer symbol and is related to the Shintani--Barnes double sine function and the Faddeev quantum dilogarithm. We prove a refinement of Shintani's Kronecker limit formula that relates square roots of Stark class invariants to real multiplication values of the cocycle, which are cohomological invariants.

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Gene S. Kopp. 2025-05-03. The Shintani--Faddeev modular cocycle: Stark units from $q$-Pochhammer ratios. https://arxiv.org/abs/2411.06763

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