From the 1 of 6 linked papers with an AI index.
6 papers
Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere
Claire Burrin, Matthias Gröbner
The paper studies how rational points of fixed height are distributed on the two‑dimensional sphere at shrinking scales, proving variance and equidistribution results that match ra…
Murmurations in the depth aspect
Claire Burrin, Vivian Kuperberg, Min Lee +2
We compute the murmuration density function for the family of Hecke forms of weight and prime power level , with a fixed odd prime and .
A Human Story of Curiosity and Relevance
Claire Burrin
Mathematics is changing. Computers are verifying proofs, checking calculations, and exploring complex structures that would overwhelm human effort. Yet curiosity-driven research is…
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…
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…
Equidistribution of continuous low-lying pairs of horocycles via Ratner's theorem
Claire Burrin
We record an alternative proof of a recent joint equidistribution result of Blomer and Michel, based on Ratner's topological rigidity theorem. This approach has the advantage of ex…