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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
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:

$\displaystyle L\left (\tfrac {1}{2}+it,\pi \right )\ll _{\pi ,\varepsilon } (1+\vert t\vert)^{\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
Email: rmunshi@math.tifr.res.in

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