The first moment of the symmetric-square L-function
The first moment of the symmetric-square L-function
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DOI：
10.1016/j.jnt.2006.09.010
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发表时间：
2007-06
影响因子：
0.7
通讯作者：
Rizwanur Khan
中科院分区：
文献类型：
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作者：
Rizwanur Khan
当k→∞时，我们在满模群的权为k的Hecke特征形f上，在临界线上的任意点s上找到L（sym2f，s）的扭一阶矩。作为推论，我们证明了给定临界线上的任何点，并且k足够大，存在一个权为k的特征形f，使得L（sym2f，s）在该点处不为零。
We find a twisted first moment of L(sym2f,s) at any point s on the critical line, over a basis of weight k Hecke eigenforms f for the full modular group, as k→∞. As a corollary we show that given any point on the critical line and large enough even k, there exists an eigenform f of weight k such that L(sym2f,s) is nonvanishing at that point.