A zero density estimate and fractional imaginary parts of zeros for ${\mathrm{GL}}_2$ $L$-functions

Olivia Beckwith, Di Liu, Jesse Thorner +1

We prove an analogue of Selberg's zero density estimate for $\zeta (s)$ that holds for any ${\mathrm{GL}}_2$ $L$-function. We use this estimate to study the distribution of the vector of…