The Gauss Sphere Problem

Fan Zheng, Princeton University
Fine Hall 314

The Gauss Sphere Problem is a long-open problem in analytic number theory concerning the number of lattice points in a sphere. In this talk I will discuss a variant of this problem: that of summing a polynomial over the lattice points in a sphere. We will use tools from Fourier analysis, exponential sums and modular forms, to sharpen our estimates step by step.