论文标题
autour del'énumérationdes repredeSentations cuspidalesalgébriquesde $ {\ rm gl} _n $ sur $ \ mathbb {q}
Autour de l'énumération des représentations automorphes cuspidales algébriques de ${\rm GL}_n$ sur $\mathbb{Q}$ de conducteur $>1$
论文作者
论文摘要
我们证明了$ {\ rm gl} _n $ of $ \ mathbb {q} $（$ n $ nutionary）的小型指挥和小动机重量的caspidal自动形态代数表示的分类结果，本着Chenevier，Lannes和Taïbi的工作精神。主要结果是所有此类表示的明确列表，其动机重量高达$ 17 $，指挥家$ 2 $。为此，我们基于Riemann-Weil显式公式开发了分析方法，并使用Arthur的工作将这些表示形式与经典对象联系起来。一个关键成分是关于split $ {\ rm so} _ {2n+1}（\ Mathbb {q} _p）$的splate $ {\ rm so} _ {\ rm so} _ {\ rm so} _ {\ rm so} _ {\ rm so} _的特殊情况，我们也证明了这一点。
We prove classification results for the cuspidal automorphic algebraic representations of ${\rm GL}_n$ over $\mathbb{Q}$ ($n$ arbitrary) of small prime conductor and small motivic weight, in the spirit of the works of Chenevier, Lannes and Taïbi in conductor $1$. The main result is an explicit list of all such representations with motivic weight up to $17$ and conductor $2$. For this, we develop the analytical method based on the Riemann-Weil explicit formulas, and use Arthur's work to relate those representations to classical objects. A key ingredient is a special case of Gross' conjecture regarding paramodular invariants of representations of a split ${\rm SO}_{2n+1}(\mathbb{Q}_p)$, which we prove as well.
