Let ℓ be a prime and let L/ℚ be a Galois number field with Galois group isomorphic to ℤ/ℓℤ . We show that the shape of L, see Definition 1.2, is either 12𝔸ℓ−1 or a fixed sub-lattice depending only on ℓ ; 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 ℤ/3ℤ number fields.
The shape of ℤ/ℓℤ-number fields
Monsurro' M
2016-01-01
Abstract
Let ℓ be a prime and let L/ℚ be a Galois number field with Galois group isomorphic to ℤ/ℓℤ . We show that the shape of L, see Definition 1.2, is either 12𝔸ℓ−1 or a fixed sub-lattice depending only on ℓ ; 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 ℤ/3ℤ number fields.File in questo prodotto:
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