Modular forms of rational weights and modular varieties
Modular forms of rational weights and modular varieties
复制标题
合理权重和模块化品种的模块化形式
DOI：
10.1007/bf02940923
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
T. Ibukiyama
中科院分区：
文献类型：
--
作者：
T. Ibukiyama
最近，BANNAI等人[2]在有限酉反射群理论的启发下，系统地研究了一元模形式的多项式环。在这项工作中，作者给出了一个意见，即有理权重的模形式是有趣的对象，表明属于5级主同余子群的权重k/5的模形式的环是由两个权重为1/5的元素生成的。(This与克莱因在世纪的工作有一定的联系。他们在[2]中的工作是一个相当”手工制作”的个案研究。这篇论文是由他们的工作激发的。本文对任意大于3的奇整数N，给出了属于主同余子群的一元有理权（N-3）/2N（具有一定乘子系）模形式的系统构造
Recently, BANNAI and others [2], partly motivated by the theory of finite unitary reflection groups, systematically investigated rings of modular forms of one variables which are polynomial rings. In that work, the authors gave a remark that modular forms of rational weights are interesting objects, showing that the ring of modular forms of weights k/5 belonging to the principal congruence subgroup of level 5 is generated by two elements of weight 1/5.(This has some connection with KLEIN'S work in the 19-th century.) Their work in [2] is a rather" hand-made" case-by-case study. This paper is motivated by their work. In this paper, for any odd integer N> 3, we give some systematic construction of modular forms of one variable of rational weight (N-3)/2N (with a certain multiplier system) belonging to the principal congruence subgroup