This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of . We shall study how many such angles may appear in a given lattice and in which positions, allowing the lattice to vary arbitrarily. This classification turns out to be much less simple than could be expected, leading even to parametrizations involving rational points on certain algebraic curves of positive genus.

Classification of rational angles in plane lattices

Umberto Zannier
2022

Abstract

This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of . We shall study how many such angles may appear in a given lattice and in which positions, allowing the lattice to vary arbitrarily. This classification turns out to be much less simple than could be expected, leading even to parametrizations involving rational points on certain algebraic curves of positive genus.
2022
Settore MAT/03 - Geometria
Plane lattices; trigonometric diophantine equations; rational points on curves
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/110048
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