论文标题
较高重量的刚性分析共生的Shimura-Shintani对应关系
A Shimura-Shintani correspondence for rigid analytic cocycles of higher weight
论文作者
论文摘要
本文迈出了第一步，朝着对更高重量的添加性刚性混蛋进行系统的研究。这些是由达尔蒙（Darmon）和沃克（Vonk）引入的，他们专注于乘法和重量两个同伴。在对某些僵硬的杂型共体重量分类后，重量$ 2K $，我们构建了一个明确的全态核函数，实现了Shimura-shintani风格的对应关系，来自重量$ k+1/2 $的模块形式，$ k+1/2 $和级别$ 4p^2 $固定的分析cocycles to sl $ _2 $ 2k $ $ _2（k）$ 2k $} $ _2（k）$ _2（\ zb）[
This paper takes the first steps towards a systematic study of additive rigid meromorphic cocycles of higher weight. These were introduced by Darmon and Vonk, who focused on multiplicative and weight two cocycles. After classifying certain rigid meromorphic cocycles of weight $2k$, we construct an explicit holomorphic kernel function realising a Shimura-Shintani style correspondence from modular forms of weight $k+1/2$ and level $4p^2$ to rigid analytic cocycles of weight $2k$ on SL$_2(\mathbb{Z}[1/p])$.
