11 citations · 39 across the 17 of their papers we have counts for
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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 .
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…
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…
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…
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…