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

no code implementations • 2 Mar 2021 • Olivia Beckwith, Di Liu, Jesse Thorner, Alexandru Zaharescu

We prove an analogue of Selberg's zero density estimate for $\zeta(s)$ that holds for any $\mathrm{GL}_2$ $L$-function.

Number Theory

Exceptional characters and nonvanishing of Dirichlet $L$-functions

no code implementations • 8 Dec 2020 • H. M. Bui, Kyle Pratt, Alexandru Zaharescu

Let $\psi$ be a real primitive character modulo $D$.

Number Theory