$\psi(N,\chi)=-N^{\beta_1}/\beta_1+O(N e^{-c_1\sqrt{\log N}})$ for non-principal $\chi$, given the zero-free region

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$\psi(N,\chi)=-N^{\beta_1}/\beta_1+O(N e^{-c_1\sqrt{\log N}})$ for non-principal $\chi$, given the zero-free region · Prove2Me