论文标题
扭曲$ gl（2）$短字符总和的子左强度界限
Sub-Weyl strength bounds for twisted $GL(2)$ short character sums
论文作者
论文摘要
令$$ s（n）= \ sum_ {n \ sim n}^{\ text {smooke}} \，λ_{f}（n）\，χ（n），$$ 其中$λ_{f}（n）$是hecke-eigen表单的傅立叶系数，而$χ$是导体$ p^{r} $的原始特征。在本文中，我们证明了$ s（n）$的子方强度界限。确实，我们获得了 $ s（n）\ ll \，n^{\ frac {5} {9}}} \ p^{\ frac {13r} {45}}，$$ 前提是$ p^{13r/20} \ leq n \ leq p^{4r/5} $。请注意，如果$ n \ geq \ left（p^{r} \ right）^{\ frac {2} {3} {3} - \ frac {1} {60} {60}} $，则上述限制为$ s（n）$是非平地的。
Let $$S(N) = \sum_{n \sim N}^{\text{smooth}} \, λ_{f}(n) \, χ(n),$$ where $λ_{f}(n)$'s are Fourier coefficients of Hecke-eigen form, and $χ$ is a primitive character of conductor $p^{r}$. In this article we prove a sub-Weyl strength bounds for $S(N)$. Indeed, we obtain $$S(N) \ll \, N^{\frac{5}{9}} \ p^{\frac{13r}{45}},$$ provided that $ p^{13r/20} \leq N \leq p^{4r/5}$. Note that the above bound for $S(N)$ is non-trivial if $N\geq \left(p^{r}\right)^{\frac{2}{3}-\frac{1}{60}}$.
