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.
2016
Number fields
Shape
Lattices
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14092/1124
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