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Explore the intricacies of bounding moments of character sums in this 49-minute lecture by Adam James Harper at BIMSA. Delve into the problem of bounding power averages of sums $\sum_{n \leq x} \chi(n)$, where $\chi$ varies over all non-principal Dirichlet characters mod $r$. Focus on the "low moments" (up to the second moment) and discover how they are expected to be modeled by corresponding moments of Steinhaus random multiplicative functions. Gain insights into the current knowledge in the random setting and learn how this understanding can be applied to the deterministic character sum setting. If time allows, examine a potential application to non-vanishing, providing a comprehensive overview of this complex mathematical topic.
