论文标题
关于三个产品L功能和Harris-venkatesh的猜想
On triple product L-functions and a conjecture of Harris--Venkatesh
论文作者
论文摘要
Harris和Venkatesh在体重一个模块化形式的环境中提出了一个猜想，该猜想与派生的Hecke操作员和伴奏动机同胞相关。在二面案例中，达尔蒙 - harris-rotger-venkatesh证明了这种猜想。我们使用一种新方法来证明猜想的更一般情况（直至签名）。我们的方法依赖于Waldspurger的公式来证明Rankin L系列的核心价值和Ichino的三级产品L功能的公式。
Harris and Venkatesh made a conjecture relating the derived Hecke operators and the adjoint motivic cohomology in the setting of weight one modular forms. This conjecture was proved under some conditions in the dihedral case by Darmon--Harris--Rotger--Venkatesh. We use a new approach to prove more general cases of the conjecture (up to sign). Our approach relies on Waldspurger's formula for the central value of Rankin L-series and Ichino's formula for the triple product L-function.
