3 papers
math.NT2026
Eisenstein circle packings and the Eisenpint Schmidt arrangement
James Rickards, Katherine E. Stange
The Schmidt arrangement of an imaginary quadratic number field is the orbit of the extended real line under as Möbius transformations on the ext…
math.NT2026
Division polynomials for arbitrary isogenies
Katherine E. Stange
Following work of Mazur-Tate and Satoh, we extend the definition of division polynomials to arbitrary isogenies of elliptic curves, including those whose kernels do not sum to the…
math.NT2024
An illustrated introduction to the arithmetic of Apollonian circle packings, continued fractions, and other thin orbits
Katherine E. Stange
These notes cover and expand upon the material for two summer schools: The first, which was held at CIRM, Marseille, France, July 10-14, 2023, as part of "Renormalization and Visua…