论文标题
Bianchi模块化形式的多重性的尖锐边界
Sharp bounds for multiplicities of Bianchi modular forms
论文作者
论文摘要
我们证明，在任何数字字段上，在$ \ mathrm {sl} _2 $上对固定水平的共同体自动形式的空间的维度和不完全真实的$ \ mathrm {sl} _2 $增长。特别是，我们建立了尖锐的双安奇模块化形式的生长。我们通过将Ardakov和Wadsley的代数微钙化应用于完整的同源性，将问题转移到有关完整的通用包围代数的问题中。我们证明，在微电位化下，我们证明有限生成的iWasawa模块是通用的，它通过估计Poincaré-Birkhoff-Witt Witt过滤在此类模块上的增长来解决代表理论问题。
We prove a degree-one saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on $\mathrm{SL}_2$ over any number field that is not totally real. In particular, we establish a sharp bound on the growth of cuspidal Bianchi modular forms. We transfer our problem into a question over the completed universal enveloping algebras by applying an algebraic microlocalisation of Ardakov and Wadsley to the completed homology. We prove finitely generated Iwasawa modules under the microlocalisation are generic, solving the representation theoretic question by estimating growth of Poincaré-Birkhoff-Witt filtrations on such modules.
