A new subconvex bound for $\rm GL(3)$ $L$-functions in the $t$-aspect

Keshav Aggarwal

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arXiv · 1903.09638

A new subconvex bound for $\rm GL(3)$ $L$-functions in the $t$-aspect

Keshav Aggarwal

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Abstract

We revisit Munshi's proof of the $t$-aspect subconvex bound for $\rm GL(3)$ $L$-functions, and we are able to remove the `conductor lowering' trick. This simplification along with a more careful stationary phase analysis allows us to improve Munshi's bound to, $$ L(1/2+it, \pi) \ll_{\pi, \epsilon} (1+|t|)^{3/4-3/40+\epsilon}. $$

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Keshav Aggarwal. 2019-03-23. A new subconvex bound for $\rm GL(3)$ $L$-functions in the $t$-aspect. https://arxiv.org/abs/1903.09638

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