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

本课题将研究GL2和GL3的l -不变量和p进自同构形式的几个重要问题。第一个中心目标是探索Bergdall-Pollack的鬼猜想和l不变量取值猜想之间的关系，包括计算和理论。第二个目标是证明GL3在p进域上的某些p进自同构形式的一个新的非临界性命题，它暗示了著名的amice - v<s:1>和Vishik定理的一个类似。这反过来又可以用来实现本提议的第三个目标：在更高权重形式的秩3情况下构建teitelbaum风格的l -不变量。

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.