Let ${\mathfrak{F}}_n$ be the set of cuspidal automorphic representations π of ${\mathrm{GL}}_n$ over a number field with unitary central character. We prove two unconditional large sieve inequalities for the Hecke eigenvalues of $\pi \in {\mathfrak{F}}_n$, one on the integers and one on the primes. The second leads to the first unconditional zero density estimate for the family of L-functions $L(s,\pi )$ associated to $\pi \in {\mathfrak{F}}_n$, which we make log-free. As an application of the zero density estimate, we prove a hybrid subconvexity bound for $L(\frac{1}{2},\pi )$ for a density one subset of $\pi \in {\mathfrak{F}}_n$.

中文翻译：

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无条件GL _n大筛

让 ${\mathfrak{F}}_{ñ}$是集尖点自守表示的π的${\mathrm{GL}}_{ñ}$在具有单一中心字符的数字字段上。我们证明了Hecke特征值的两个无条件大筛子不等式$\pi \in {\mathfrak{F}}_{ñ}$，一个在整数上，一个在质数上。第二个导致L函数族的第一个无条件零密度估计$\mathrm{大号}（s，\pi ）$ 关联到 $\pi \in {\mathfrak{F}}_{ñ}$，我们使它免日志。作为零密度估计的应用，我们证明了$\mathrm{大号}（\frac{\mathrm{1个}}{2}，\pi ）$ 对于一个密度的子集 $\pi \in {\mathfrak{F}}_{ñ}$。