CAI Yuanqing
Associate Professor
Classifiying periodic functions
Department of Mathematics, Mathematics
Theme | Automorphic representations on reductive groups and their covering groups |
Field | Number theory, representation theory |
Keyword | automorphic 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
Doubling constructions: global functoriality for non-generic cuspidal representations
Ann. of Math. to appear.
Twisted doubling integrals for Brylinski-Deligne extensions of classical groups
J. Inst. Math. Jussieu 22 (2023), pp. 1931-1985.
Doubling constructions and tensor product L-functions: the linear case
Invent. Math. 217 (2019), pp. 985-1068.
Fourier coefficients for Theta representations on covers of general linear groups
Trans. Amer. Math. Soc. 371 (2019), pp. 7585-7626.