Speaker
Bryce Kerr, University of New South Wales
Abstract
Heath-Brown showed that the abc-conjecture implies one may improve the Weyl exponent for cubic exponential sums with a quadratic irrational phase. I’ll outline an argument which establishes Heath-Brown’s result unconditionally. By combining ideas of Enflo and Heath-Brown with the q van der Corput method, we reduce to complete exponential sums which may be estimated to arbitrary modulus as opposed to Heath-Brown which requires the modulus to be squarefree.