论文标题
吉田升降机的第一个负特征值
The first negative eigenvalue of Yoshida lifts
论文作者
论文摘要
我们证明，对于任何给定的$ε> 0 $，这是Yoshida Lift $ f $的第一个负面特征值，一对椭圆形的cusp formp $ f，g $具有无平方的水平（其中$ g $具有$ 2 $ $ 2 $，满足$（\ log log q_ {g}） ε} $;其中$ q_f，q_f，q_g $分别是$ f，f，g $的分析导体，$θ<1/4 $，$c_ε$仅取决于$ε$。
We prove that for any given $ε>0$, the first negative eigenvalue of the Yoshida lift $F$ of a pair of elliptic cusp forms $f,g$ having square-free levels (where $g$ has weight $2$ and satisfies $(\log Q_{g})^2 \ll \log Q_f$), occurs before $c_ε \cdot Q_F^{1/2-2 θ+ ε} $; where $Q_F,Q_f,Q_g$ are the analytic conductors of $F,f,g$ respectively, $θ< 1/4$, and $c_ε$ is a constant depending only on $ε$.
