论文标题
模块化形式的关键点
Critical points of modular forms
论文作者
论文摘要
我们计算模块化形式的临界点的数量，并在标准基本域$ \ mathcal {f} $的$γ$ - 跨层中具有真实的傅立叶系数（带有$γ\ in \ Mathrm {sl} _2 _2 _2 _2（\ Mathbb {z}）$）。而按价式，该模块化形式的（加权）以$γ\ Mathcal {f} $的（仅取决于其重量的不同）的零数量，我们给出了$ \ nathcal {f}边界上的模块化形式的零件的封闭公式，以$ \ \ \ \ \ f}的边界为$ f}，$ groun $ umpry $γ^^。更普遍地，我们指出了关于准形式的零数的说法。
We count the number of critical points of a modular form with real Fourier coefficients in a $γ$-translate of the standard fundamental domain $\mathcal{F}$ (with $γ\in \mathrm{SL}_2(\mathbb{Z})$). Whereas by the valence formula the (weighted) number of zeros of this modular form in $γ\mathcal{F}$ is a constant only depending on its weight, we give a closed formula for this number of critical points in terms of those zeros of the modular form lying on the boundary of $\mathcal{F},$ the value of $γ^{-1}(\infty)$ and the weight. More generally, we indicate what can be said about the number of zeros of a quasimodular form.
