A note on Shintani's invariant
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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Finite Group Theory Research
Advanced Topics in Algebra
Publication details
- Journal / source
- Functiones et Approximatio Commentarii Mathematici
- Publisher
- Adam Mickiewicz University (Euclid)
- Volume
- -1
- Issue
- -1
- Pages
- 1–15
- Publication date
- 1 January 2026
- Language
- EN