David Lowry-Duda

Recent progress on the generalized Gauss Circle Problem, and related topics

The Gauss Circle problem concerns estimating the number of integer points contained within a circle or radius R centered at the origin. For large R, the number of points is very nearly the area of the circle, but the error term appears to be much smaller than expected. The generalized Gauss Circle problem refers to the analogous problem in dimension 3 or more. Using the theory of modular forms and theta functions, it is possible to tackle these problems. In this talk, I describe ideas and techniques leading to improved understanding of these error terms, as well as related topics concerning sums of coefficients of modular forms. This talk includes some joint work with Chan Ieong Kuan, Thomas Hulse of Morgan State, and Alex Walker of Brown University.