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Isotropic N-Point Basis Functions and Their Properties

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arxiv 2010.14418 v1 pith:QECPO2FC submitted 2020-10-27 astro-ph.CO math-phmath.MP

classification astro-ph.COmath-phmath.MP
keywords functionsbasisisotropicconvenientlypropertiesadditionalgebraicanalyzing
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abstract

Isotropic functions of positions $\hat{\bf r}_1, \hat{\bf r}_2,\ldots, \hat{\bf r}_N$, i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch-Gordan coefficients. An orthonormal basis of such functions provides a formalism suitable for analyzing isotropic distributions such as those that arise in cosmology, for instance in the clustering of galaxies as revealed by large-scale structure surveys. The algebraic properties of the basis functions are conveniently expressed in terms of 6-$j$ and 9-$j$ symbols. The calculation of relations among the basis functions is facilitated by "Yutsis" diagrams for the addition and recoupling of angular momenta.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. No evidence for parity violation in BOSS

    astro-ph.CO 2024-07 unverdicted novelty 7.0 of 10

    New statistics applied to BOSS data show the reported parity violation signal is consistent with zero after accounting for eight-point correlation function mismatch between data and mocks.

  2. Probing Parity Violation with Weak Lensing Trispectrum

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    A parity-odd weak lensing convergence trispectrum is derived and forecast to be detectable with DES Y3/LSST Y10-like surveys under optimistic template amplitudes.

  3. Parity-odd Four-Point Correlation Function from DESI Data Release 1 Luminous Red Galaxy Sample

    astro-ph.CO 2025-12 accept novelty 6.0 of 10

    The parity-odd four-point correlation function measured in DESI DR1 LRGs is consistent with zero after correcting for survey-induced covariance mismatches.

  4. Measurement of Parity-Violating Modes of the Dark Energy Spectroscopic Instrument (DESI) Year 1 Luminous Red Galaxies' 4-Point Correlation Function

    astro-ph.CO 2025-08 conditional novelty 6.0 of 10

    DESI's first parity-violation search shows a strong auto-correlation signal that disappears when the sky is split into patches, pointing to underestimated mocks' variance rather than new physics.

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