In this talk we will continue to our discussion of the paper "Fourier Analytic Techniques for Lattice Point Discrepancy" by Luca Brandolini and Giancarlo Travaglini. In particular we will use the pointwise and L^p-average decay estimates on Fourier transforms of indicators of convex bodies proved in the two previous seminar sessions to bound L^p norms of the discrepancy function over translations and over translations and rotations.
Reference: L. Brandolini, G. Travaglini. "Fourier analytic techniques for lattice point discrepancy." Discrepancy theory 26 (2020).