Subconvexity for $GL_{3}(R)$ $L$-Functions via Integral Representations

Raphael Schumacher

Published 2020-04-14Version 1

We study the subconvexity problem for $GL_{3}(R)$ $L$-functions in the t-aspect using integral representations by combining techniques employed by Michel--Venkatesh in their study of the corresponding problem for $GL_{2}$ with ideas from recent works of Munshi, Holowinsky--Nelson and Lin. Our main objective is to explain in detail the origin of the "key identity" arising in the latter series of works from the perspective of integral representations of $L$-functions and automorphic representation theory.