标题： 对称平方$L$函数的周期线性无关性 显示英文标题

标题： Linear independence of periods for the symmetric square $L$-functions

摘要： 对于$S_k$，权为$k$的全模群的尖点形式空间，我们首先引入与对称平方$L$-函数相关的$S_k$上的周期。 我们然后证明，对于固定的自然数$n$，如果$k$相对于$n$足够大，那么任何$n$的这样的周期都是线性无关的。 在一些额外假设下，我们也证明，对于$k\geq e^{12}$，我们可以总是选取最多$\frac{\log k}{4}$个任意的线性无关周期。 显示英文摘要

摘要： For $S_k$, the space of cusp forms of weight $k$ for the full modular group, we first introduce periods on $S_k$ associated to symmetric square $L$-functions. We then prove that for a fixed natural number $n$, if $k$ is sufficiently large relative to $n$, then any $n$ such periods are linearly independent. With some extra assumption, we also prove that for $k\geq e^{12}$, we can always pick up to $\frac{\log k}{4}$ arbitrary linearly independent periods.