论文标题
重量2极度谐波maass形式$ h_ {n，z}^*（τ）$
The Completed $L$-function attached to the Weight 2 Polar Harmonic Maass Form $H_{N,z}^*(τ)$
论文作者
论文摘要
在本文中，我们研究了重量2级$ n $ harmonic maass形式的梅林变换$ h_ {n，z}^*（τ）$，并分析此（广义）$ l $ - 功能为$ \ mathrm {imrm {im}（z）\ to \ infty $。在途中，我们还计算了$ h_ {n，z}^*（τ）$的傅立叶扩展，以$γ_0（n）$的任意振尖，我们将功能方程式和分解为$ l $ l $ function的本地因素，用于$ n $ n $ eisenstein系列，在Cusps $ i \ iffty $ i \ iffty和$ 0. $ n $ eisenstein系列中。
In this paper, we study the Mellin transform of the weight 2 level $N$ polar harmonic Maass form $H_{N,z}^*(τ)$, and analyze this (generalized) $L$-function as $\mathrm{Im}(z)\to \infty$. On the way, we also calculate the Fourier expansion of $H_{N,z}^*(τ)$ at arbitrary cusps of $Γ_0(N)$, and we give a functional equation and factorization into local factors of the $L$-function for the weight 2 level $N$ Eisenstein series at the cusps $i\infty$ and $0$.
