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Hankel transform, Langlands functoriality and functional equation of automorphic L-functions

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Abstract

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.

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Acknowledgements

This paper may be seen as a progress report of a longterm project on the Langlands functoriality. In the course of this reflection, I have benefited many insights from discussions with A. Altug, J. Arthur, B. Casselman, T. H. Chen, S. Cheng, V. Drinfeld, J. Getz, D. Jiang, D. Johnstone, T. Kaletha, R. Langlands, G. Laumon, Y. Sakellaridis, F. Shahidi and Z. Yun. Thanks are also due to my students J. Chi and X. Wang who have proofread the manuscript. I thank heartily the referee for his/her careful reading of the manuscript and comments. This work is partially supported by the Simons foundation and the NSF grant DMS-1702380.

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  1. Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL, 60637-1514, USA

    Bảo Châu Ngô

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Communicated by: Takeshi Saito

Dedicated to the memory of Prof. Hiroshi Saito, with affection

This article is based on the 18th Takagi Lectures that the author delivered at The University of Tokyo on November 5–6, 2016.

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Ngô, B.C. Hankel transform, Langlands functoriality and functional equation of automorphic L-functions. Jpn. J. Math. 15, 121–167 (2020). https://doi.org/10.1007/s11537-019-1650-8

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  • DOI: https://doi.org/10.1007/s11537-019-1650-8

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