Let $K$ be a number field, $\mathfrak{ q}$ be an integral ideal, and $\mathrm{ Cl}(\mathfrak{ q})$ be the associated ray class group. Suppose $\mathrm{ Cl}(\mathfrak{ q})$ possesses a real exceptional character $\psi$, possibly principal, with a Siegel zero $\beta$. For $\mathcal{ C} \in \mathrm{ Cl}(\mathfrak{ q})$ satisfying $\psi(\mathcal{ C}) = 1$, we establish an effective $K$-uniform Linnik-type bound with explicit constants for the least norm of a prime ideal $\mathfrak{ p} \in \mathcal{ C}$. A special case of this result is related to rational primes represented by certain binary quadratic forms.
Categories: math.NT