Perturbations of Weyl sums, and uniform distribution mod 1
Seminar Room 1, Newton Institute
AbstractSignificant advances in our understanding of mean values of exponential sums have resulted from recent progress in Vinogradov's mean value theorem, in particular as a consequence of efficient congruencing methods. These advances lead to improved pointwise estimates for Weyl sums. In this talk we will explore the consequences of such ideas for perturbed exponential sums in which lower degree coefficients are permitted to vary over a set of large measure. The conclusions we obtain are related to recent work of Livio Flaminio and Giovanni Forni.
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