Simultaneous nonvanishing of automorphic L-functions at the central point
Simultaneous nonvanishing of automorphic L-functions at the central point
复制标题
中心点自守 L 函数同时不为零
DOI：
10.1007/s00229-010-0396-7
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发表时间：
2011
影响因子：
0.6
通讯作者：
Zhao Xu
中科院分区：
文献类型：
--
作者：
Zhao Xu
设g是全纯Hecke本征形，{uj}是$${\textup{SL}(2，\mathbb{Z})}$$的偶数Hecke-Maass形式的正交基。表示L(S，g×uj)和L(S，uj)对应的L函数。本文给出了平均$${L(FRAC{1}{2}，g次u_j)L(\FRAC{1}{2}，u_j)}$$的渐近公式，由此我们得到了无穷多个Uj使得$${L(\FRAC{1}{2}，g\x u_j)L(\FRAC{1}{2}，u_j)}$$.
Let g be a holomorphic Hecke eigenform and {uj} an orthonormal basis of even Hecke–Maass forms for $${\textup{SL}(2,\mathbb{Z})}$$. Denote L(s, g × uj) and L(s, uj) the corresponding L-functions. In this paper, we give an asymptotic formula for the average of $${L(\frac{1}{2},g\times u_j)L(\frac{1}{2},u_j)}$$, from which we derive that there are infinitely many uj’s such that $${L(\frac{1}{2},g\times u_j)L(\frac{1}{2},u_j)\neq0}$$.