Extreme Values of Dirichlet L-Functions At Critical Points of the Zeta Function

Abstract

Abstract We estimate large and small values of $|L(\rho^{\prime},\chi)|$, where χ is a primitive character mod q for q > 2 and $\rho^{\prime}$ runs over critical points of the Riemann zeta function in the right half of the one-line and on the one-line, that is, the points where $\zeta^{\prime}(\rho^{\prime})=0$ and $1\leq\Re \rho^{\prime}$.