11 citations · 39 across the 17 of their papers we have counts for
18 papers
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…
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 .
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, 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…
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…
On the crossing number of arithmetic curve systems
Sebastian Baader, Claire Burrin, Luca Studer
We show that the family of systoles of hyperbolic surfaces associated with congruence lattices in have asymptotically minimal crossing number.
Rational points on ellipsoids and modular forms
Claire Burrin, Matthias Gröbner
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and oth…
Pairs in discrete lattice orbits with applications to Veech surfaces
Claire Burrin, Samantha Fairchild, Jon Chaika
Let , be two discrete orbits under the linear action of a lattice on the Euclidean plane. We prove a SiegelVeech-type integral formula f…
Windings of prime geodesics
Claire Burrin, Flemming von Essen
The winding of a closed oriented geodesic around the cusp of the modular orbifold is computed by the Rademacher symbol, a classical function from the theory of modular forms. In th…
Infinitely many twin prime polynomials of odd degree
Claire Burrin, Matthew Issac
While the twin prime conjecture is still famously open, it holds true in the setting of finite fields: There are infinitely many pairs of monic irreducible polynomials over $\mathb…
The Manin-Drinfeld theorem and the rationality of Rademacher symbols
Claire Burrin
For any noncocompact Fuchsian group , we show that periods of the canonical differential of the third kind associated to residue divisors of cusps are expressed in terms of Rade…
Translates of rational points along expanding closed horocycles on the modular surface
Claire Burrin, Uri Shapira, Shucheng Yu
We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface. Using spectral meth…
Effective counting for discrete lattice orbits in the plane via Eisenstein series
Claire Burrin, Amos Nevo, Rene Rühr +1
We prove effective bounds on the rate in the quadratic growth asymptotics for the orbit of a non-uniform lattice of SL(2,R), acting linearly on the plane. This gives an error bound…
Transformation laws for generalized Dedekind sums associated to Fuchsian groups
Claire Burrin, Jay Jorgenson, Cormac O'Sullivan +1
We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. Thes…
Dedekind sums, reciprocity, and non-arithmetic groups
Claire Burrin
Dedekind sums, arithmetic correlation sums that arose in Dedekind's study of the modular transformation of the logarithm of the eta-function, are surprisingly ubiquitous. Their ari…
Reciprocity of Dedekind sums and the Euler class
Claire Burrin
Dedekind sums are arithmetic sums that were first introduced by Dedekind in the context of elliptic functions and modular forms, and later recognized to be surprisingly ubiquitous.…
Generalized Dedekind sums and equidistribution mod 1
Claire Burrin
Dedekind sums are well-studied arithmetic sums, with values uniformly distributed on the unit interval. Based on their relation to certain modular forms, Dedekind sums may be defin…