论文标题
在扭曲$ l $ functions的第一时刻的错误术语中
On an error term for the first moment of twisted $L$-functions
论文作者
论文摘要
让$ f $是整个模块化组的hecke-maass尖缘形式，让$χ$成为原始的dirichlet角色modulo a Prime $ Q $。令$ s_0 =σ_0+it_0 $与$ \ frac {1} {2} {2} \leqσ_0<1 $。我们在$ l（s_0，f \ otimes黄）的第一瞬间提高了错误术语\ overline {l（s_0，χ）} $，即使是原始的dirichlet字符的家族。作为一个应用程序，我们表明，对于任何$ t \ in \ mathbb {r} $，都存在一个原始的dirichlet字符$花（1+ | t |）^{\ frac {543} {25}+\ varepsilon} $。
Let $f$ be a Hecke-Maass cusp form for the full modular group and let $χ$ be a primitive Dirichlet character modulo a prime $q$. Let $s_0=σ_0+it_0$ with $\frac{1}{2}\leqσ_0<1$. We improve the error term for the first moment of $L(s_0,f\otimesχ)\overline{L(s_0,χ)}$ over the family of even primitive Dirichlet characters. As an application, we show that for any $t\in\mathbb{R}$, there exists a primitive Dirichlet character $χ$ modulo $q$ for which $L(1/2+it,f\otimesχ)L(1/2+it,χ)\neq0$ if the prime $q$ satisfies $q\gg (1+|t|)^{\frac{543}{25}+\varepsilon}$.
