{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PTH7SXLTI57O4ZPIGFOELGQS5J","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"658554437e3a9eb8e9a19124ca9bd095abe57d9e7da12492ecd67f6f87150fe5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-10T08:34:13Z","title_canon_sha256":"e01cb56d19ca23228a550214bdeb486b3c4bb6420d6c224898b0a352f9790a0a"},"schema_version":"1.0","source":{"id":"1104.1756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1756","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1756v2","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1756","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"PTH7SXLTI57O","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PTH7SXLTI57O4ZPI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PTH7SXLT","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:6c149c4bc172694bd20e4d1dff896c388b940afa1b6bd07e1b27542f4779bd81","target":"graph","created_at":"2026-05-18T02:57:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study representation zeta functions of finitely generated, torsion-free nilpotent groups which are rational points of unipotent group schemes over rings of integers of number fields. Using the Kirillov orbit method and p-adic integration, we prove rationality and functional equations for almost all local factors of the Euler products of these zeta functions. We further give explicit formulae, in terms of Dedekind zeta functions, for the zeta functions of class-2-nilpotent groups obtained from three infinite families of group schemes, generalising the integral Heisenberg group. As an immedia","authors_text":"Alexander Stasinski, Christopher Voll","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-10T08:34:13Z","title":"Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1756","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ed0a2745d1d25d9c227ee282fb7baf01e05f574ef50f2845b3fa53ba3d75390b","target":"record","created_at":"2026-05-18T02:57:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"658554437e3a9eb8e9a19124ca9bd095abe57d9e7da12492ecd67f6f87150fe5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-10T08:34:13Z","title_canon_sha256":"e01cb56d19ca23228a550214bdeb486b3c4bb6420d6c224898b0a352f9790a0a"},"schema_version":"1.0","source":{"id":"1104.1756","kind":"arxiv","version":2}},"canonical_sha256":"7ccff95d73477eee65e8315c459a12ea5226c06f9032dcaceb0bb60970edd9cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ccff95d73477eee65e8315c459a12ea5226c06f9032dcaceb0bb60970edd9cc","first_computed_at":"2026-05-18T02:57:44.273032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:44.273032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pFppDhA+m9yCMaZVtB3CxgvXzHVLICLRxKoUCTZeKHYFt+3ku5bNavgmqJwFsU4ikjbH7J0lKnVyXJHYqQIpBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:44.273563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed0a2745d1d25d9c227ee282fb7baf01e05f574ef50f2845b3fa53ba3d75390b","sha256:6c149c4bc172694bd20e4d1dff896c388b940afa1b6bd07e1b27542f4779bd81"],"state_sha256":"5ef8035b44c3f819d3d377ac20bb330256031db303873bd0bdf6a75d702bcb9c"}