论文标题
Rankin-Selberg $ L $ functions和DeLigne猜想的应用程序比率的代数
Algebraicity of ratios of Rankin-Selberg $L$-functions and applications to Deligne's conjecture
论文作者
论文摘要
在本文中，我们证明了Deligne对与重量大于四的模块化形式相关的对称功率$ l $ functions的临界值的代数。 We also prove new cases of Blasius' conjecture on the algebraicity of critical values of tensor product $L$-functions associated to modular forms, and an algebraicity result on critical values of Rankin-Selberg $L$-functions for ${\rm GL}_n \times {\rm GL}_2$ in the unbalanced case, which extends the previous results of Furusawa and $ {\ rm so}（v）\ times {\ rm gl} _2 $。这些是我们主要结果的应用，这是兰金·塞尔伯格$ l $ functions特殊值比率的代数。
In this paper, we prove Deligne's conjecture on the algebraicity of critical values of symmetric power $L$-functions associated to modular forms of weight greater than four. We also prove new cases of Blasius' conjecture on the algebraicity of critical values of tensor product $L$-functions associated to modular forms, and an algebraicity result on critical values of Rankin-Selberg $L$-functions for ${\rm GL}_n \times {\rm GL}_2$ in the unbalanced case, which extends the previous results of Furusawa and Morimoto for ${\rm SO}(V) \times {\rm GL}_2$. These are applications of our main result on the algebraicity of ratios of special values of Rankin-Selberg $L$-functions.
