Long Liu

Extreme values of quadratic Hecke $L$-functions

We study large values of quadratic Hecke $L$-functions in the conductor aspect. Let $K$ be a fixed number field, and assume GRH for its finite-order Hecke $L$-functions. In a fixed ray class component with conductor norm comparable to $X$, we prove that \[ \max_\chi L\left(\frac12+\frac A{\log_2X},\chi\right) \geq\exp\...