The shape of $$ \mathbb {Z}/\ell \mathbb {Z}$$-number fields |
| |
Authors: | Guillermo Mantilla-Soler Marina Monsurrò |
| |
Institution: | 1.Departamento de Matemáticas,Universidad de los Andes,Bogotá,Colombia;2.Università Eropea di Roma,Rome,Italy |
| |
Abstract: | Let \(\ell \) be a prime and let \(L/ \mathbb {Q}\) be a Galois number field with Galois group isomorphic to \( \mathbb {Z}/\ell \mathbb {Z}\). We show that the shape of L, see Definition 1.2, is either \(\frac{1}{2}\mathbb {A}_{\ell -1}\) or a fixed sub-lattice depending only on \(\ell \); such a dichotomy in the value of the shape only depends on the type of ramification of L. This work is motivated by a result of Bhargava and Shnidman, and a previous work of the first named author, on the shape of \( \mathbb {Z}/3 \mathbb {Z}\) number fields. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|