The mean square of real character sums

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.

11 pages. arXiv admin note: text overlap with arXiv:0907.4747 by other authors

References in corpus (1)

• The first moment of quadratic Dirichlet L-functions