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arXiv · 2408.07309

A note on Shintani's invariants

Bora Yalkinoglu
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Abstract

Shintani's celebrated invariants are conjectured to generate abelian extensions of real quadratic number fields, offering a potential solution to Hilbert's 12th problem in that setting. In this note, we derive new expressions for Shintani's invariants by generalizing an observation of Yamamoto, who showed that these invariants - originally formulated using the double sine function - can be expressed in terms of the q-Pochhammer symbol.

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Bora Yalkinoglu. 2026-02-06. A note on Shintani's invariants. https://doi.org/10.7169/facm%2F250808-31-12

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