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arXiv · 2509.24152

Short Interval Variance and Averaged Correlations of Arithmetic Functions

Jiseong Kim
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Abstract

In this paper, we study the average shifted sum for general arithmetic functions by applying the standard Hardy--Littlewood circle method and using short-interval variance results. As applications, we prove some nontrivial upper bounds for shifted sums involving $\mu_{k}(n).$ Assuming the Riemann Hypothesis and the Pair Correlation Conjecture of Montgomery, we also prove similar results involving the von Mangoldt function.

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Jiseong Kim. 2025-09-29. Short Interval Variance and Averaged Correlations of Arithmetic Functions. https://arxiv.org/abs/2509.24152

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