论文标题
矩和混合亚凸，用于对称平方的L功能
Moments and hybrid subconvexity for symmetric-square L-functions
论文作者
论文摘要
我们在hecke maass cusp forms $ u_j $带有频谱参数$ t_j $的对称平方$ l $ functions的第二瞬间建立了尖锐的界限，其中第二瞬间是短时间间隔$ t_j $的总和。在中央点$ s = 1/2 $的$ l $ function，我们的间隔小于以前的已知结果。更具体地说，对于$ | t_j | $ size $ t $的$，我们的间隔为$ t^{1/5} $，而以前的最佳是$ t^{1/3} $，来自LAM的工作。在临界线上稍高一点，我们的第二刻为对称平方$ l $ unction绑定了一个子峰值。更具体地说，我们在$ s = 1/2+it $ subconvexity $ | t_j |^{6/7+δ} \ le | t | \ le（2-δ）| t_j | $对于任何固定的$δ> 0 $。由于$ | t | $可以显着小于$ | t_j | $，因此可以将其视为与频谱方面的对称方面$ l $ function的臭名昭著的子凸问题的近似值。
We establish sharp bounds for the second moment of symmetric-square $L$-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$, where the second moment is a sum over $t_j$ in a short interval. At the central point $s=1/2$ of the $L$-function, our interval is smaller than previous known results. More specifically, for $|t_j|$ of size $T$, our interval is of size $T^{1/5}$, while the previous best was $T^{1/3}$ from work of Lam. A little higher up on the critical line, our second moment yields a subconvexity bound for the symmetric-square $L$-function. More specifically, we get subconvexity at $s=1/2+it$ provided $|t_j|^{6/7+δ}\le |t| \le (2-δ)|t_j|$ for any fixed $δ>0$. Since $|t|$ can be taken significantly smaller than $|t_j|$, this may be viewed as an approximation to the notorious subconvexity problem for the symmetric-square $L$-function in the spectral aspect at $s=1/2$.
