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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_χL\left(\frac12+\frac A{\log_2X},χ\r
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