论文标题
遗传学模块化形式的某些代数的不繁殖
Nonfreeness of some algebras of hermitian modular forms
论文作者
论文摘要
我们研究晶格$ l_n = diag（1,1，\ ldots，1，-1）$的庇护自动形式的代数，对于$ k = \ mathbb {q}（\ sqrt {-d}）$我们证明，对于$ d> 7 $，这些代数不能免费。当$ d = 7 $和$ d = 3 $时，我们对这些代数可能是免费的对称空间的维度进行了估算。我们还将结果与已知结果进行比较，$ d = 3 $。
We study the algebras of hermitian automorphic forms for the lattice $L_n=diag(1,1,\ldots,1,-1)$ and for the field $K=\mathbb{Q}(\sqrt{-d})$ such that $p=2$ is unramified and the ring of integers $\mathcal{O}_K$ is a p.i.d. We prove that for $d>7$ these algebras can't be free. When $d=7$ and $d=3$ we give an estimate for the dimension of the symmetric spaces for which these algebras might be free. We also compare our results with the known results for $d=3$.
