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arXiv · 2212.09241

Mean squares of quadratic twists of the M\"obius function

Peng Gao·Liangyi Zhao
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Abstract

In this paper, we evaluate asymptotically the sum \[ \sum_{d \leq X} \left( \sum_{n \leq Y} \mu(n)\leg {8d}{n} \right)^2, \] where $\leg {8d}{n}$ is the Kronecker symbol and $d$ runs over positive, odd, square-free integers.

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Peng Gao, Liangyi Zhao. 2022-12-19. Mean squares of quadratic twists of the M\"obius function. https://doi.org/10.1016/j.jnt.2022.12.007

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