Burgess bounds for short character sums in new settings

Burgess bounds for short character sums in new settings

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Lillian Pierce, Duke University
Fine Hall 214

In the late 1950’s, Burgess developed a novel method for bounding short sums of a multiplicative Dirichlet character. This resulted in a subconvexity bound for Dirichlet L-functions on the critical line. In recent work with Roger Heath-Brown, we have adapted the Burgess method to prove bounds for character sums in more general settings, and in particular via an unexpected application of the Vinogradov Mean Value Theorem. We will survey aspects of this work and the accompanying new results.