论文标题
扭曲三重产品$ l $ functions的中心关键价值的代数
Algebraicity of the central critical values of twisted triple product $L$-functions
论文作者
论文摘要
我们研究了在完全不平衡的情况下，在完全不平衡的情况下，与动机希尔伯特·库斯普（Hilbert Cusp）相关的扭曲三级产品$ l $ runctions的中心临界值的代数。代数是根据哈里斯（Harris）开发的Quaternionic Shimura品种构建的共同体学时期表示的。作为一个应用程序，我们将以前的结果推广到Deligne的猜想，以$ {\ rm gl} _3 \ times {\ rm gl} _2 $。我们还建立了代数Hecke角色扭曲下的共同体学期间的关系。
We study the algebraicity of the central critical values of twisted triple product $L$-functions associated to motivic Hilbert cusp forms over a totally real étale cubic algebra in the totally unbalanced case. The algebraicity is expressed in terms of the cohomological period constructed via the theory of coherent cohomology on quaternionic Shimura varieties developed by Harris. As an application, we generalize our previous result on Deligne's conjecture for certain automorphic $L$-functions for ${\rm GL}_3 \times {\rm GL}_2$. We also establish a relation for the cohomological periods under twisting by algebraic Hecke characters.
