We consider the moment of quadratic twists of the M\"obius function of the form \[ S_k(X,Y) = ∑d≤ X ( ∑n≤ Y (8d/n) μ(n))^k, \] where (8d/·) is the Kronecker symbol and d runs over positive, odd and square-free integers. We give unconditional results for their asymptotic behaviors.
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Yuichiro Toma (2024) studied this question.
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