A note on Shintani's invariants
Number Theory
2026-02-09 v3
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.
Cite
@article{arxiv.2408.07309,
title = {A note on Shintani's invariants},
author = {Bora Yalkinoglu},
journal= {arXiv preprint arXiv:2408.07309},
year = {2026}
}
Comments
accepted final version, some improvements