This is a survey on recent works of Langlands’s work on functoriality conjectures and related works including the works of Braverman and Kazhdan on the functional equation of automorphic L-functions. Efforts have been made to carry out in complete generality the construction of the L-monoid, and certain a kernel which is, we believe, related to the elusive Hankel kernel.

中文翻译：

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Hankel 变换、Langlands 函子性和自守 L 函数的函数方程

这是对 Langlands 关于函子性猜想的最新著作以及相关著作（包括 Braverman 和 Kazhdan 关于自守L函数的泛函方程）的著作的综述。人们已经做出了努力来完全普遍地构建L-幺半群，以及我们相信与难以捉摸的汉克尔核相关的某些核。