Dimensions of automorphic representations, L-functions and liftings
Dimensions of automorphic representations, L-functions and liftings
复制标题
自守表示、L 函数和提升的维数
DOI：
10.1007/978-3-030-68506-5_3
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Ginzburg, David
中科院分区：
文献类型：
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作者：
Friedberg, Solomon;Ginzburg, David
有许多Rankin-Selberg积分表示LanglandsL-函数，并且不清楚Rankin-Selberg方法的限制是什么。维数方程是许多这样的积分所满足的等式，这表明了进一步研究的优先权。然而，也有Rankin-Selberg积分不满足这个方程。在这里，我们提出了一个扩展和重新制定的尺寸方程，包括许多额外的情况。我们解释了其中的一些情况下，包括新的加倍积分的作者，蔡和卡普兰。然后，我们将展示如何使用相同的方程来理解θ提升，以及如何将加倍积分融入提升框架。我们举一个例子，一种新型的电梯，这是自然的从这个角度来看。
There are many Rankin-Selberg integrals representing LanglandsL-functions, and it is not apparent what the limits of the Rankin-Selberg method are. The Dimension Equation is an equality satisfied by many such integrals that suggests a priority for further investigations. However there are also Rankin-Selberg integrals that do not satisfy this equation. Here we propose an extension and reformulation of the dimension equation that includes many additional cases. We explain some of these cases, including the new doubling integrals of the authors, Cai and Kaplan. We then show how this same equation can be used to understand theta liftings, and how doubling integrals fit into a lifting framework. We give an example of a new type of lift that is natural from this point of view.