L-invariants and p-adic automorphic forms in ranks 2 and 3

2 阶和 3 阶中的 L 不变量和 p 进自守形式

• 批准号: 491064713
• 负责人: Dr. Peter Mathias Gräf
• 金额: --
• 依托单位: Department of Mathematics and Statistics
• 依托单位国家: 德国
• 项目类别: WBP Fellowship
• 财政年份: 2021
• 资助国家: 德国
• 起止时间: 2020-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/491064713?language=en
• 关键词: invariants; adic; automorphic; forms; ranks

In this project several important questions centered on L-invariants and p-adic automorphic forms for GL2 and GL3 shall be investigated. The first central goal is to explore relations between the ghost conjecture of Bergdall-Pollack and conjectures on valuations of L-invariants, both computationally and theoretically. The second goal is to prove a new non-criticality statement for certain p-adic automorphic forms for GL3 over p-adic fields, which implies an analogue of the well-known theorem of Amice-Vélu and Vishik. This in turn can be used to achive the third goal of this proposal: the construction of Teitelbaum-style L-invariants in the rank-3 situation for forms of higher weight.

在这个项目中，几个重要的问题集中在L-不变量和p-adic自守形式的GL 2和GL 3将被调查。第一个中心目标是探索Bergdall-Pollack的幽灵猜想和L-不变量的估值之间的关系，无论是计算上还是理论上。第二个目标是证明p-adic域上GL 3的某些p-adic自守形式的一个新的非临界性陈述，这意味着Amice-Vélu和Visik的著名定理的类似物。这反过来又可以用来实现这个提议的第三个目标：在秩3的情况下，构造更高权重形式的Teitelbaum式L-不变量。