Just a little idea that I suddenly remembered but realized I don’t exactly remember now. So writing it down for memory.

Given two polynomials $p,q$ where $${z: |p(z)|=1} = {z:|q(z)| = 1}$$ show that $p=\xi^n,q=c\xi^m$ for some polynomial $\xi$ and $|c| = 1$.

Some thoughts that I had while trying a bunch of problems.

Problem. Show that for two circles $\omega_1,\omega_2$, the locus of points which are of a constant power ratio to both circles is also a circle (or line) coaxal to the both circles.

The last part of a 3-part series on Analytic NT. Part III is about Fourier stuff.

In this part we take a quick tour through Fourier things (and why they appear here) as well as a bunch of neat looking facts (no proofs!).