What question did this study set out to answer?

The aim is to prove a joint equidistribution for Hecke-Maaß cusp forms in hyperbolic three-space.

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February 19, 2026Open Access

Joint distribution of Hecke eigenforms on H3 H³

Q: What does this research mean for the field?

Hecke–Maaß cusp forms on hyperbolic three-space exhibit joint value equidistribution, supporting the conjectural statistical independence of orthogonal cusp forms. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.SUPPORTS_CONSENSUS.

Key Points

The aim is to prove a joint equidistribution for Hecke-Maaß cusp forms in hyperbolic three-space.
Analyzed the joint distribution of Hecke eigenforms in H3
Utilized concepts from number theory and geometry
Applied statistical methods to assess independence
Established a joint value equidistribution for Hecke–Maaß cusp forms
Provided evidence supporting statistical independence of these forms
Contributed to understanding of cusp forms on hyperbolic spaces

Abstract

Abstract We prove a joint value equidistribution statement for Hecke–Maaß cusp forms on the hyperbolic three‐space . This supports the conjectural statistical independence of orthogonal cusp forms.

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