Effective log-free zero density estimates for automorphic $L$-functions and the Sato-Tate conjecture

Robert J. Lemke Oliver, Jesse Thorner

Let $K/\mathbb{Q}$ be a number field. Let $\pi$ and ${\pi }^{\prime }$ be cuspidal automorphic representations of ${\mathrm{GL}}_d({\mathbb{A}}_K)$ and ${\mathrm{GL}}_{d^{\prime }}({\mathbb{A}}_K)$, an…