Lemma 3.2 . [0425]

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Lemma 3.2.

Let $|x|=|\text{Re}(\eta)|\leq\frac{1}{2}$ . The difference $\tilde{\alpha}_{i}-\alpha_{i}$ satisfies the estimate

|\tilde{\alpha}_{i}-\alpha_{i}|\leq CA^{-1/4}\log(1+A^{-1/2}|\vec{\mu}|_{a}).