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Here s denotes a complex variable and Z(G,s) is defined as the Dirichlet generating function whose nth coefficient is equal to the number of irreducible characters of G of degree n. For p greater than 2 it is known that Z(G,s) defines a meromorphic function on the complex plane.\n  Wedderburn's structure theorem for semisimple algebras implies that ZG,-2) = |G|"},"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":"1302.5566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-22T12:14:25Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7ff7c7524b48d0c586e356ceb0b4dc0d5d855e40c8f28fcff02ab292e54e4000","abstract_canon_sha256":"b4f366c9a505ed8ba75c8ef1e72611707c54e1844128e9a06a27f66b226b8b85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.001727Z","signature_b64":"mGTm7miIQMrovjUII0wLUKGa1geXOyhlNehUq772VAFDVQuCTvhPiplNkCvtPGLRmhyf/cQvcI87xADyq0LTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fa939ab947797cbc8a8d493d47a944166b0d425d5967d545547a8b987231ab5","last_reissued_at":"2026-05-18T00:44:30.001130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.001130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The representation zeta function of a FAb compact p-adic Lie group vanishes at -2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.GR","authors_text":"Andrei Jaikin-Zapirain, Benjamin Klopsch, Jon Gonzalez-Sanchez","submitted_at":"2013-02-22T12:14:25Z","abstract_excerpt":"Let G by compact p-adic Lie group and suppose that G is FAb, i.e., that H/[H,H] is finite for every open subgroup H of G. 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