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.
Here are the slides for my talk.
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.
Info on how to comment
To make a comment, please send an email using the button below. Your email address won't be shared (unless you include it in the body of your comment). If you don't want your real name to be used next to your comment, please specify the name you would like to use. If you want your name to link to a particular url, include that as well.
bold, italics, and plain text are allowed in comments. A reasonable subset of markdown is supported, including lists, links, and fenced code blocks. In addition, math can be formatted using
$(inline math)$or$$(your display equation)$$.Please use plaintext email when commenting. See Plaintext Email and Comments on this site for more. Note also that comments are expected to be open, considerate, and respectful.