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

Raphael Schumacher

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arXiv · 2004.06791

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

Raphael Schumacher

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Abstract

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 give - from the perspective of integral representations of $L$-functions and automorphic representation theory - a possible explanation of the origin of the "key identity" arising in the latter series of works.

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Raphael Schumacher. 2020-04-14. Subconvexity for $GL_{3}(R)$ $L$-Functions: The Key Identity via Integral Representations. https://arxiv.org/abs/2004.06791

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