A generalized hermite constant for imaginary quadratic fields
We introduce the projective Hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field K. It is a lower bound for the classical Hermite constant, and these two constants coincide when K has class number one. Using the geometric tools developed b...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/51828 |
| Acceso en línea: | http://hdl.handle.net/11336/51828 |
| Access Level: | acceso abierto |
| Palabra clave: | Extreme Hermitian Forms Hermite Constant Minima of Hermitian Forms https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/1.2 |
| Sumario: | We introduce the projective Hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field K. It is a lower bound for the classical Hermite constant, and these two constants coincide when K has class number one. Using the geometric tools developed by Mendoza and Vogtmann for their study of the homology of the Bianchi groups, we compute the projective Hermite constants for those K whose absolute discriminants are less than 70, and determine the hermitian forms that attain the projective Hermite constants in these cases. A comparison of the projective hermitian constant with some other generalizations of the classical Hermite constant is also given. |
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