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M\\\"oller and the author found a factorization of the Selberg zeta function into a product of Fredholm determinants of transfer-operator-like families: $Z(s) = \\det(1-\\mc L_s^+)\\det(1-\\mc L_s^-)$. In this article we show that the operator families $\\mc L_s^\\pm$ arise as families of transfer operators for the triangle groups underlying the Hecke triangle groups, and that for $s\\in\\C$, $\\Rea s=\\tfrac12$, the operator $\\mc L_s^+$ (resp. $\\mc L_s^-$) has a 1-eigenfunction if and "},"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":"1303.0528","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-03T16:52:45Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"c9e8b2152588f53e4dbf4925e68755dc66a498f6ee7ab38e95d22c30f7b3622e","abstract_canon_sha256":"bcfa05acb5e91e27a6aa8f6782555687a22fe1341f0376b0981bd0da91ab9956"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:40.428662Z","signature_b64":"VqKIShV6MHudsBf0ZdMao6ePpeknY8gcyPLnsA+3jJQAoQK6m29Zyh6ttywn+bbehApX5ww+8mI75Uf8ZvMTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c0df477d0785a7ee1f45c9a8d5a5b0c5569522deb36854f92d2f9bf7c0a35bd","last_reissued_at":"2026-05-18T01:23:40.428105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:40.428105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.SP","authors_text":"Anke D. 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