Mathematics > Number Theory
[Submitted on 1 Mar 2025
]
Title: Sub-Weyl bound for $GL(2)$ via trivial delta
Title: $GL(2)$的平凡 delta 的次 Weyl 界
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-\delta+\varepsilon}, \end{equation*} where $\delta=1/174$, 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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