AI 中文总结
本文针对数域F上GL₂的简单超尖分歧尖自守表示，建立了Weyl型次凸性界，证明了相关四阶矩估计，推导得出Weyl型界，且该界适用于三次矩方法无法处理的真正非自对偶族。
AI 中文摘要
我们建立了数域F上GL₂的尖自守表示在素理想𝔮处具有简单超尖分歧时，在水平方向的Weyl型次凸性界。更确切地说，对于由导子为𝔮³、中心特征为ω且具有指定简单超尖局部分量的表示族ℱ_t^ζ(𝔮³;ω)，我们证明了四阶矩估计：∑_{π∈ℱ_t^ζ(𝔮³;ω) \ C_v(π)≤𝐂_v, v|∞} |L(1/2,π)|⁴ ≪_{F,ε} 𝐂_∞^{1+ε} N_F(𝔮)^{2+ε}。由此推导出Weyl型界：L(1/2,π) ≪_{F,ε} C_∞(π)^{1/4+ε} C_fin(π)^{1/6+ε}。特别地，该界适用于一类奇导子指数的真正非自对偶族，超出了三次矩方法的适用范围。
英文摘要
We establish Weyl-type subconvexity bounds in the level aspect for cuspidal automorphic representations of $\mathrm{GL}_2/F$ with simple supercuspidal ramification at a prime ideal $\mathfrak{q}$. More precisely, for the family $\mathcal{F}_t^ζ(\mathfrak{q}^3;ω)$ consisting of representations of conductor $\mathfrak{q}^3$, central character $ω$, and prescribed simple supercuspidal local component, we prove the fourth moment estimate \begin{align*} \sum_{\substack{π\in \mathcal{F}_{t}^ζ(\mathfrak{q}^3;ω) \\ C_v(π) \leq \mathbf{C}_v,\ v \mid \infty}} |L(1/2,π)|^4 \ll_{F,\varepsilon} \mathbf C_\infty^{1+\varepsilon} N_F(\mathfrak{q})^{2+\varepsilon}. \end{align*} As a consequence, we deduce the Weyl-type bound \begin{align*} L(1/2,π) \ll_{F,\varepsilon} C_{\infty}(π)^{1/4+\varepsilon} C_{\mathrm{fin}}(π)^{1/6+\varepsilon}. \end{align*} In particular, this bound applies to a genuinely non-self-dual family of odd conductor exponent, beyond the reach of the cubic moment method.
Comments54 pages
