The circle method and bounds for 𝐿-functions—III: 𝑡-aspect subconvexity for 𝐺𝐿(3) 𝐿-functions

Munshi, Ritabrata

doi:10.1090/jams/843

The circle method and bounds for $L$-functions—III: $t$-aspect subconvexity for $GL(3)$ $L$-functions
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by Ritabrata Munshi

J. Amer. Math. Soc. 28 (2015), 913-938

DOI: https://doi.org/10.1090/jams/843

Published electronically: July 13, 2015

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Abstract:

Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb {Z})$. In this paper we will prove the following subconvex bound: \[ L\left (\tfrac {1}{2}+it,\pi \right )\ll _{\pi ,\varepsilon } (1+|t|)^{\frac {3}{4}-\frac {1}{16}+\varepsilon }. \]

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