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math.GT2025
Modular systoles are extremal for the crossing number
Claire Burrin, Hugo Parlier
We study crossing numbers for systoles of congruence surfaces. Taken as a family of curves on a family of surfaces, we show that the growth rate of their intersection is optimally…
math.DS2025
The Brjuno and Wilton Functions
Claire Burrin, Seul Bee Lee, Stefano Marmi
The Brjuno and Wilton functions bear a striking resemblance, despite their very different origins; while the Brjuno function is a fundamental tool in one-dimensional holomor…
math.NT2025
Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere
Claire Burrin, Matthias Gröbner
We study the distribution of rational points of fixed height on the sphere at shrinking scales. For the two-dimensional sphere, we prove an unconditional variance estimate for prim…