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Journal of the American Mathematical Society

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


Author: Ritabrata Munshi
Journal: J. Amer. Math. Soc. 28 (2015), 913-938
MSC (2010): Primary 11F66, 11M41; Secondary 11F55
DOI: https://doi.org/10.1090/jams/843
Published electronically: July 13, 2015
MathSciNet review: 3369905
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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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Additional Information

Ritabrata Munshi
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, 1 Dr. Homi Bhabha Road, Colaba, Mumbai 400005, India
MR Author ID: 817043
Email: rmunshi@math.tifr.res.in

Keywords: Subconvexity, $GL(3)$ Maass forms, twists
Received by editor(s): March 31, 2014
Published electronically: July 13, 2015
Article copyright: © Copyright 2015 American Mathematical Society