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arXiv · 2503.00656

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

Roman Holowinsky·Ritabrata Munshi·Prahlad Sharma·Jakob Streipel
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Abstract

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

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Roman Holowinsky, Ritabrata Munshi, Prahlad Sharma, Jakob Streipel. 2025-03-01. Sub-Weyl bound for $GL(2)$ via trivial delta. https://arxiv.org/abs/2503.00656

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