On the class number of the genus of $\mathbb{Z}$-maximal lattices with respect to quadratic form of the sum of squares
Hiraoka, Takahiro
J. Math. Kyoto Univ., Tome 46 (2006) no. 4, p. 291-302 / Harvested from Project Euclid
In this paper we consider the quadratic form $\phi [x] = \sum _{i=1}^{n} x_{i}^{2}$ over the vector space $\mathbb{Q}_{n}^{1}$. We take a $\mathbb{Z}$-maximal lattice $L$ in $\mathbb{Q}_{n}^{1}$ with respect to $\phi$. Let $\{L^{(i)}\}_{i=1}^{k(n)}$ be a complete set of representatives for the classes belonging to the genus of $L$. Applying Shimura's mass formula, we determine these representatives $L^{(i)}$ explicitly for $n = 11, 13$, and $14$. Consequently we obtain class numbers $k(11) = 3$, $k(13) = 4$, and $k(14) = 4$.
Publié le : 2006-05-15
Classification:  11E41,  11E12
@article{1250281778,
     author = {Hiraoka, Takahiro},
     title = {On the class number of the genus of $\mathbb{Z}$-maximal lattices with respect to quadratic form of the sum of squares},
     journal = {J. Math. Kyoto Univ.},
     volume = {46},
     number = {4},
     year = {2006},
     pages = { 291-302},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250281778}
}
Hiraoka, Takahiro. On the class number of the genus of $\mathbb{Z}$-maximal lattices with respect to quadratic form of the sum of squares. J. Math. Kyoto Univ., Tome 46 (2006) no. 4, pp.  291-302. http://gdmltest.u-ga.fr/item/1250281778/