I’m currently at an AIM workshop on Arithmetic Statistics, Discrete Restriction, and Fourier Analysis. This morning (AIM time)/afternoon (USEast time), I’ll be giving a talk on Lattice points and sums of Fourier Coefficients of modular forms.
The theme of this talk is embodied in the statement that several lattice counting problems like the Gauss circle problem are essentially the same as very modular-form-heavy problems, sometimes very closely similar and sometimes appearing slightly different.
In this talk, I describe several recent adventures, successes and travails, in my studies of problems related to the Gauss circle problem and the task of producing better bounds for the sum of the first several coefficients of holomorphic cuspforms.
I’ll note that various parts of this talk have appeared in several previous talks of mine, but since it’s the pandemic era this is the first time much of this has appeared in slides.