Non-vanishing of Dirichlet $L$-functions with Moduli in Short Intervals
and Arithmetic Progressions
Non-vanishing of Dirichlet $L$-functions with Moduli in Short Intervals
and Arithmetic Progressions
Assuming the Generalized Riemann Hypothesis, it is known that at least half of the central values $L(\frac{1}{2},\chi)$ are non-vanishing as $\chi$ ranges over primitive characters modulo $q$. Unconditionally, this is known on average over both $\chi$ modulo $q$ and $Q/2 \leq q \leq 2Q$. We prove that for any $\delta>0$, …