Greenberg's conjecture for real quadratic number fields
We compute the 3-class groups A_n of the fields F_n in the cyclotomic Z_3-extensions of the real quadratic fields of discriminant f < 100,000. In all cases the orders of A_n remain bounded as n goes to infinity. This is in agreement with Greenberg's conjecture.
Authors
- Pietro Mercuri (ORCID: https://orcid.org/0000-0003-4402-6432)
- René Schoof (ORCID: https://orcid.org/0000-0003-1375-2458)
- Maurizio Paoluzi
Institutions
- University of Rome Tor Vergata (IT)
- University of Trento (IT)
Publication Details
- Journal
- Journal of Experimental Mathematics
- Published
- 2025-08-30
- DOI
- https://doi.org/10.56994/jxm.001.002.001
- Citations
- 1
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Sapienza Università di Roma
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni