On the variance of sums of divisor functions in short intervals

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Given a positive integer n the k-fold divisor function dₖ(n) equals the number of ordered k-tuples of positive integers whose product equals n. In this article we study the variance of sums of dₖ(n) in short intervals and establish asymptotic formulas for the variance of sums of dₖ(n) in short intervals of certain lengths for k=3 and for k ≥ 4 under the assumption of the Lindelöf hypothesis.