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A ring of symmetric Hermitian modular forms of degree 2 with integral Fourier coefficients
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ( IF 0.4 ) Pub Date : 2019-09-03 , DOI: 10.1007/s12188-019-00205-8
Toshiyuki Kikuta

We determine the structure over $\mathbb{Z}$ of the ring of symmetric Hermitian modular forms with respect to $\mathbb{Q}(\sqrt{-1})$ of degree $2$ (with a character), whose Fourier coefficients are integers. Namely, we give a set of generators consisting of $24$ modular forms. As an application of our structure theorem, we give the Sturm bounds of such the modular forms of weight $k$ with $4\mid k$, in the case $p=2$, $3$. We remark that the bounds for $p\ge 5$ are already known.

中文翻译:

具有积分傅立叶系数的 2 次对称厄米模形式的环

我们确定关于 $\mathbb{Q}(\sqrt{-1})$ 的阶数为 $2$(带有一个字符)的对称 Hermitian 模形式环的 $\mathbb{Z}$ 上的结构,其傅立叶系数是整数。也就是说,我们给出了一组由 $24$ 模块化形式组成的生成器。作为我们的结构定理的应用,我们给出了这种权重 $k$ 的模形式的 Sturm 边界,其中 $4\mid k$,在 $p=2$,$3$ 的情况下。我们注意到 $p\ge 5$ 的边界是已知的。
更新日期:2019-09-03
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