PreprintCC BY-SA 4.0arXiv
On ℤ2-extensions of real quadratic fields
Abstract
Let k be a real quadratic field. Let kn be the n-th layer of the ℤ2-extension of k, and 2an be the $2$-part of the class number of kn. In this paper, we derive many laws concerning the sequence (a0,a1,dotsc), by iteratively extending the group of cyclotomic units.
Related
- On ℤ2-extensions of real quadratic fields with class group of $2$-rank three
- Maximal unramified 3-extensions of imaginary quadratic fields and \textrm SL\sb 2(\mathbb Z\sb 3)
- Torsion groups of rational elliptic curves over ℤp-extensions of quadratic fields: the p≤ 5 case
- Torsion growth of rational elliptic curves over Zp-extensions of quadratic fields
- Shimura Reciprocity for Real Quadratic Fields
BibTeX
@misc{sasaki2026ℤ2extensions,
title = {{On $\mathbbZ_2$-extensions of real quadratic fields}},
author = {Sosuke Sasaki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.00482},
eprint = {2606.00482},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.00482},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - On ℤ_2-extensions of real quadratic fields
AU - Sosuke Sasaki
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2606.00482
UR - https://arxiv.org/abs/2606.00482
AB - Let k be a real quadratic field. Let k_n be the n-th layer of the ℤ_2-extension of k, and 2^a_n be the $2$-part of the class number of k_n. In this paper, we derive many laws concerning the sequence (a_0,a_1,dotsc), by iteratively extending the group of cyclotomic units.
ER -