Artículos de revistas
A generalized hermite constant for imaginary quadratic fields
Fecha
2015-01Registro en:
Chan, Wai Kiu; Icaza, María Inés; Lauret, Emilio Agustin; A generalized hermite constant for imaginary quadratic fields; American Mathematical Society; Mathematics Of Computation; 84; 294; 1-2015; 1883-1900
0025-5718
CONICET Digital
CONICET
Autor
Chan, Wai Kiu
Icaza, María Inés
Lauret, Emilio Agustin
Resumen
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.