Shuichiro TAKEDA

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number theory, representation theory
Keywords automorphic representations, automorphic forms, representations of p-adic groups

One of the important objects of study in modern number theory is automorphic representations and their L-functions. An automorphic representation is a representation of a certain matrix group, normally known as reductive group, and considered as a vast generalization of classical modular forms. An automorphic representation further decomposes into their local counterparts, which are representations of reductive groups over local fields, in particular p-adic groups. I have been studying various relations among these representations, especially by using the theory known as theta correspondence. The theory of theta correspondence allows one to construct a representation of one group out of another, and thus to compare representations of different groups. Using this theory, I have obtained numerous interesting results in the theory of automorphic representations and their related themes.