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

Keshav Aggarwal

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

Number Theory 2020-01-31 v3

Authors: Keshav Aggarwal

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, $L(1/2+it, \pi) \ll_{\pi, \epsilon} (1+|t|)^{3/4-3/40+\epsilon}.$

Keywords

gl(3) l-functions subconvex bound t-aspect stationary phase analysis automorphic forms

Cite

@article{arxiv.1903.09638,
  title  = {A new subconvex bound for $\rm GL(3)$ $L$-functions in the $t$-aspect},
  author = {Keshav Aggarwal},
  journal= {arXiv preprint arXiv:1903.09638},
  year   = {2020}
}

Comments

19 pages; Corrected errors and made revisions to the stationary phase analysis

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