English

Sub-Weyl bound for $GL(2)$ via trivial delta

Number Theory 2025-03-04 v1

Abstract

For a SL(2,Z)SL(2,\mathbb{Z}) form ff, we obtain the sub-Weyl bound \begin{equation*} L(1/2+it,f)\ll_{f,\varepsilon} t^{1/3-\delta+\varepsilon}, \end{equation*} where δ=1/174\delta=1/174, thereby crossing the Weyl barrier for the first time beyond GL(1)GL(1). The proof uses a refinement of the `trivial' delta method.

Keywords

Cite

@article{arxiv.2503.00656,
  title  = {Sub-Weyl bound for $GL(2)$ via trivial delta},
  author = {Roman Holowinsky and Ritabrata Munshi and Prahlad Sharma and Jakob Streipel},
  journal= {arXiv preprint arXiv:2503.00656},
  year   = {2025}
}
R2 v1 2026-06-28T22:03:18.641Z