English

$t$-aspect subconvexity for $GL(2)$ $L$-functions

Number Theory 2017-10-05 v2

Abstract

Let ff be a holomorphic cusp form for SL2(Z)SL_2(\mathbb{Z}) of weight k>1k>1. In these notes, we follow Munshi to prove the Burgess bound L(1/2+it,f)f,ε(1+t)1/21/8+ε. L(1/2+it,f)\ll_{f,\varepsilon} (1+|t|)^{1/2-1/8+\varepsilon}.

Keywords

Cite

@article{arxiv.1707.07027,
  title  = {$t$-aspect subconvexity for $GL(2)$ $L$-functions},
  author = {Keshav Aggarwal},
  journal= {arXiv preprint arXiv:1707.07027},
  year   = {2017}
}

Comments

Typos corrected, and a mistake taken care of in section 5. The result is unchanged

R2 v1 2026-06-22T20:54:21.209Z