Researcher Information

CAI Yuanqing

Associate Professor

Classifiying periodic functions

Department of Mathematics, Mathematics

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Theme

Automorphic representations on reductive groups and their covering groups

FieldNumber theory, representation theory
Keywordautomorphic L-functions, automorphic representations, covering groups

Introduction of Research

Automorphic representations and their L-functions carry important arithmetic information and are still actively research subjects. Many research results have been discovered through the theta correspondence and the doubling method. The aim of my research is to develop the local and global theories of automorphic L-functions of classical groups through a generalization of the doubling method.

Moreover, the theory of automorphic representations of Brylinski-Deligne covering groups (BD covering groups) of reductive groups has also attracted attention in recent years. I am also interested in the theories of automorphic L-functions and automorphic representations of BD covering groups.

Representative Achievements

Yuanqing Cai, Solomon Friedberg and Eyal Kaplan
Doubling constructions: global functoriality for non-generic cuspidal representations
Ann. of Math. to appear.
Yuanqing Cai
Twisted doubling integrals for Brylinski-Deligne extensions of classical groups
J. Inst. Math. Jussieu 22 (2023), pp. 1931-1985.
Yuanqing Cai, Solomon Friedberg, David Ginzburg and Eyal Kaplan
Doubling constructions and tensor product L-functions: the linear case
Invent. Math. 217 (2019), pp. 985-1068.
Yuanqing Cai
Fourier coefficients for Theta representations on covers of general linear groups
Trans. Amer. Math. Soc. 371 (2019), pp. 7585-7626.