Stolarsky’s invariance principle for projective spaces

doi:10.1016/j.jco.2019.101428

Journal of Complexity

Volume 56, February 2020, 101428

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Abstract

We show that Stolarsky’s invariance principle, known for point distributions on the Euclidean spheres, can be extended to the real, complex, and quaternionic projective spaces and the octonionic projective plane.

Keywords

Projective spaces

Geometry of distances

Discrepancies

Spherical functions

Jacobi polynomials

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^☆: This work is supported by the Program of the Presidium of the Russian Academy of Sciences “New Methods of Mathematical Modeling in the Study of Nonlinear Dynamical Systems” under Grant PRAS 08-04.

^☆☆: Communicated by J. Dick.

Journal of Complexity

Stolarsky’s invariance principle for projective spaces☆,☆☆

Abstract

Keywords