论文标题
$ {\ rm gl} _3 \ times {\ rm gl} _2 $
A cohomological interpretation of archimedean zeta integrals for ${\rm GL}_3\times {\rm GL}_2$
论文作者
论文摘要
通过研究Eichler的明确形式 - shimura地图，以$ {\ rm gl} _3 $进行描述，我们描述了rankin-selberg卷积$ {\ rm gl} _3 _3 \ time coholy coh的完整$ l $ function的关键值之间的精确关系从所考虑的尖齿自动形式表示中，从有理标量倍数到理性的标量倍数。这是根据Raghuram等人引起的临界值的理性结果。
By studying an explicit form of the Eichler--Shimura map for ${\rm GL}_3$, we describe a precise relation between critical values of the complete $L$-function for the Rankin--Selberg convolution ${\rm GL}_3 \times {\rm GL}_2$ and the cohomological cup product of certain rational cohomology classes which are uniquely determined up to rational scalar multiples from the cuspidal automorphic representations under consideration. This refines rationality results on critical values due to Raghuram et al.
