Abstract:

Under the framework of the measure theoretic point of view, recently the asymptotic properties of Weyl sums have attracted strong attention. The Lebesgue measure theory and the Hausdorff dimension theory of the asymptotic properties for Weyl sums are core issues. In this talk we first introduce Weyl sums and show its applications in number theory and PDE. Then we show some recent achievements on measure theory of Weyl sums. This is based on joint work with Roger Baker and Igor Shparlinski.