论文标题
自动形态$ l $ functions的加权平均值
Weighted average values of automorphic $L$-functions
论文作者
论文摘要
令$ s_2^*（q）$是重量2和Prime Level $ Q $的原始Hecke特征形式的集合。对于$ p $ prime和$ t \ in \ mathbb {r} $，我们证明了总和$$ $ \ mathcal {a}（p^j，q，q，t）= \ sum_ {f \ in S_2^*（q）}的渐近公式 L\left(\frac{1}{2}+it,f\right)^2λ_f(p^j),\qquad j=1,2, $$ where $λ_f(p^j)$ is the $p^j$-th normalized Fourier coefficient of $f$ and $L(s,f)$ is the $L$-function associated to $f$.
Let $S_2^*(q)$ be the set of primitive Hecke eigenforms of weight 2 and prime level $q$. For $p$ prime and $t\in \mathbb{R}$, we prove asymptotic formulas for the sums $$ \mathcal {A}(p^j,q,t)=\sum_{f\in S_2^*(q)} L\left(\frac{1}{2}+it,f\right)^2λ_f(p^j),\qquad j=1,2, $$ where $λ_f(p^j)$ is the $p^j$-th normalized Fourier coefficient of $f$ and $L(s,f)$ is the $L$-function associated to $f$.
