论文标题
模块化形式的sturm型界限与功能字段
Sturm-type bounds for modular forms over functions fields
论文作者
论文摘要
在本文中，我们获得了在功能场设置中的模块化形式结合的Sturm的两个类似物。在混合特性的情况下，我们证明任何谐波的双层链都是由明确数量的第一个傅立叶系数的有限数量确定的，在这些傅立叶系数中，我们的界限比文献中的界限要小得多。 Hecke代数的发电机在谐波线圈上得出了类似的结合。作为一个应用程序，我们提出了一个计算标准，用于检查有理函数字段上的两条椭圆曲线$ \ mathbb {f} _q（θ）$与同一导体是等不良的。在同等特征的情况下，我们还证明，任何德林菲尔德模块化形式都是由$ t $扩展中的明确数量的第一个系数明确确定的。
In this paper, we obtain two analogues of the Sturm bound for modular forms in the function field setting. In the case of mixed characteristic, we prove that any harmonic cochain is uniquely determined by an explicit finite number of its first Fourier coefficients where our bound is much smaller than the ones in the literature. A similar bound is derived for generators of the Hecke algebra on harmonic cochains. As an application, we present a computational criterion for checking whether two elliptic curves over the rational function field $\mathbb{F}_q(θ)$ with same conductor are isogenous. In the case of equal characteristic, we also prove that any Drinfeld modular form is uniquely determined by an explicit finite number of its first coefficients in the $t$-expansion.
