Rational points on ellipsoids and modular forms

2024/01/31 by Burrin, Claire, Gröbner, Matthias
#11E25 #11F12 #11F30 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.18008

Abstract

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 other higher dimensional ellipsoids, in what may be viewed as a textbook display of the 'unreasonable effectiveness' of modular forms.

Related

• Counting rational points on the sphere with bounded denominator
• Modular forms and ellipsoidal T-designs
• Rational Points on the Unit Sphere: Approximation Complexity and Practical Constructions
• Primitive rational points on expanding horospheres in Hilbert modular surfaces
• Counting rational points on hypersurfaces and higher order expansions