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The mean square of real character sums
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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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Cited by 1 Pith paper
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Mean squares of quadratic twists of the Fourier coefficients of modular forms
An unconditional asymptotic formula is obtained for the smoothed mean square of quadratic twists of Fourier coefficients of a modular form.
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