Relative Functoriality and Functional Equations via Trace Formulas
Relative Functoriality and Functional Equations via Trace Formulas
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通过迹公式的相对函数性和函数方程
DOI：
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发表时间：
2018
影响因子：
0.5
通讯作者：
Y. Sakellaridis
中科院分区：
文献类型：
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作者：
Y. Sakellaridis
朗兰兹泛函原理预测了不同约化群的局域谱和自同构谱之间的深层关系。这已被相对朗兰兹规划推广到包括球变数，其中约化群是特殊情况。在朗兰兹“超越内窥镜”纲领的哲学中，这些关系应该被表达为不同轨迹公式之间的比较，并插入适当的l函数。l函数的插入需要实现另一个目标：通过迹公式研究它们的函数方程。本文的目的是通过实例来演示这个程序，说明内窥镜检查项目中从局部到全局的方法。在这里，标量转移因子被“转移算子”或“汉克尔变换”所取代，它们足够好（通常，可以用通常的傅里叶变换来表示），原则上可以用来证明全局比较（以泊松求和公式的形式）。其中一些例子已经出现在文献中；对其他人来说，证据会出现在其他地方。
Langlands’ functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which reductive groups are special cases. In the philosophy of Langlands’ “beyond endoscopy” program, these relations should be expressed as comparisons between different trace formulas, with the insertion of appropriate L-functions. The insertion of L-functions calls for one more goal to be achieved: the study of their functional equations via trace formulas. The goal of this article is to demonstrate this program through examples, indicating a local-to-global approach as in the project of endoscopy. Here, scalar transfer factors are replaced by “transfer operators” or “Hankel transforms” which are nice enough (typically, expressible in terms of usual Fourier transforms) that they can be used, in principle, to prove global comparisons (in the form of Poisson summation formulas). Some of these examples have already appeared in the literature; for others, the proofs will appear elsewhere.
相对迹公式之间的传递算子和 Hankel 变换，I：特征理论
影响因子：
1.7
作者：
Sakellaridis, Yiannis
通讯作者：
Sakellaridis, Yiannis
1 阶相对迹公式之间的函数传递
影响因子：
2.5
作者：
Sakellaridis, Yiannis
通讯作者：
Sakellaridis, Yiannis