论文标题
Hecke-Siegel类型的无形傅立叶系数阈值：改进
Hecke-Siegel type threshold for square-free Fourier coefficients: an improvement
论文作者
论文摘要
我们证明，如果$ f $是$γ_0（n）$的重量$ k $的一种非零CUSP形式，带有$ $χ$，以至于$ n/（\ text {contsor}χ）$ square-free-square-free，则存在一个无方形的$ n \ll_εK^{3+ε} n^n^n^n^n^n^n^n n^n ne ne $ he（这显着改善了以前的作品已知的存在和定量结果。
We prove that if $f$ is a non zero cusp form of weight $k$ on $Γ_0(N)$ with character $χ$ such that $N/(\text{conductor }χ)$ square-free, then there exists a square-free $n\ll_ε k^{3+ε}N^{7/2+ε}$ such that $a(f,n)\neq 0$. This significantly improves the already known existential and quantitative result from previous works.
