论文标题
Eichler积分和广义二阶Eisenstein系列
Eichler integrals and generalized second order Eisenstein series
论文作者
论文摘要
我们表明，所有Eichler积分，更普遍的所有“广义二阶模块形式”都可以表示为相应的广义二阶Eisenstein系列的线性组合，具有经典模块化形式的系数。我们在第一级中确定了通用二阶Eisenstein系列的傅立叶系列扩展，并通过凸度范围提供尾部估计，以添加扭曲的$ \ mathrm {l} $ - 功能。作为一个应用程序，我们说明了一个自举过程，该过程产生了仅来自关联的共生的Eichler积分的数值评估。我们的主要结果的证明取决于过滤参数，该论点主要植根于先前的矢量值模块形式的工作，我们在这里以经典的方式提出。
We show that all Eichler integrals, and more generally all "generalized second order modular forms" can be expressed as linear combinations of corresponding generalized second order Eisenstein series with coefficients in classical modular forms. We determine the Fourier series expansions of generalized second order Eisenstein series in level one, and provide tail estimates via convexity bounds for additively twisted $\mathrm{L}$-functions. As an application, we illustrate a bootstrapping procedure that yields numerical evaluations of, for instance, Eichler integrals from merely the associated cocycle. The proof of our main results rests on a filtration argument that is largely rooted in previous work on vector-valued modular forms, which we here formulate in classical terms.
