On the variance of sums of divisor functions in short intervals
5015 - 5027
Proceedings of the American Mathematical Society
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Given a positive integer n the k-fold divisor function d k (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 d k (n) in short intervals and establish asymptotic formulas for the variance of sums of d k (n) in short intervals of certain lengths for k = 3 and for k ≥ 4 under the assumption of the Lindelöf hypothesis.
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