论文标题
Eisenstein的正交组和$ l $ fors的特殊值$ {\ rm gl} _1 \ times {\ rm o}（2n）$
Eisenstein cohomology for orthogonal groups and the special values of $L$-functions for ${\rm GL}_1 \times {\rm O}(2n)$
论文作者
论文摘要
对于一个均匀的整数$ n $，我们研究了分裂正交组$ {\ rm o}（\ rm o}（2n+2）$的排名第一的爱森斯坦共同体，完全是真实的数字$ f。 \ times {\ rm o}（2n）$ of $ f $。 Case $ n = 2 $专门针对Shimura的经典结果，在Rankin的特殊值-Selberg $ L $ functions上附加了一对希尔伯特模块化表单。
For an even positive integer $n$, we study rank-one Eisenstein cohomology of the split orthogonal group ${\rm O}(2n+2)$ over a totally real number field $F.$ This is used to prove a rationality result for the ratios of successive critical values of degree-$2n$ Langlands $L$-functions associated to the group ${\rm GL}_1 \times {\rm O}(2n)$ over $F$. The case $n=2$ specializes to classical results of Shimura on the special values of Rankin - Selberg $L$-functions attached to a pair of Hilbert modular forms.
