# Colloquium: Tuesday, November 20, 2018. Speaker: Eyal Kaplan (Bar-Ilan). Title: “Doubling constructions and applications”.

Integral representations are a fundamental tool in the study of automorphic L functions.

One of these constructions, developed by Piatetski-Shapiro and Rallis in the late 80s,

produced the standard L function for any cuspidal representation of a classical group,

or its rank-1 twist. In a recent collaboration with Cai, Friedberg and Ginzburg, we extended

the doubling method to produce the tensor product L function of G X GL(k), where G

is a classical group and k is arbitrary. I will discuss recent applications of this construction

to the study of automorphic forms on classical groups as well as on covering groups.

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