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arXiv · 1908.07922

The mean square of real character sums

Peng Gao
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Abstract

In this paper, we evaluate a smoothed sum of the form $\displaystyle \sideset{}{^*}\sum_{d \leq X}\left(\sum_{n \leq Y} \left(\frac{8d}{n} \right ) \right)^2$, where $\left ( \frac{8d}{\cdot} \right )$ is the Kronecker symbol and $\sideset{}{^*}\sum$ denotes a sum over positive odd square-free integers.

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Peng Gao. 2019-08-20. The mean square of real character sums. https://arxiv.org/abs/1908.07922

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