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We show that, as the length tends to infinity, the holonomy rotations attached to these geodesics become equidistributed in $\\PSO(2)^n$ with respect to a certain measure. For the special case of lattices derived from quaternion algebras, we can give another interpretation of the holonomy angles under which this measure arises naturally."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0911.0329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-11-02T14:58:59Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d80dea97f50c741dfed02a448c1e6d03a0978ad6ad711ce030b8cf2abb2ae3f5","abstract_canon_sha256":"9af04b1ba747b6da016b560806d37628a9b8d4eff01776d7f9ee21b5c3530f02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:44.057410Z","signature_b64":"CfDvkNdaCoEkwa/4AfuzK9cSyS6+11HLXcrgarbmcssikQ5/M7W4XoBJJXuEwyA2dOiqOJRae3Qhtvy6PS1yAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"611f75a197ac0fbdcf945e588b4b3ad1a438ae93233326e313f341049ac3734b","last_reissued_at":"2026-05-18T04:41:44.057024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:44.057024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distribution of holonomy about closed geodesics in a product of hyperbolic planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Dubi Kelmer","submitted_at":"2009-11-02T14:58:59Z","abstract_excerpt":"Let $\\calM=\\Gamma\\bs \\calH^{(n)}$, where $\\calH^{(n)}$ is a product of $n+1$ hyperbolic planes and $\\Gamma\\subset\\PSL(2,\\bbR)^{n+1}$ is an irreducible cocompact lattice. 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