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These local $L$-factors decompose into a product $L^{PS}(s,\\Pi,\\Lambda)= L^{PS}_{ex}(s,\\Pi,\\Lambda) L^{PS}_{reg}(s,\\Pi,\\Lambda)$ of an exceptional and a regular $L$-factor. In this paper we compute the exceptional factors $L^{PS}_{ex}(s,\\Pi,\\Lambda)$ for split Bessel models of $\\Pi$."},"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":"1712.06370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-18T12:37:46Z","cross_cats_sorted":[],"title_canon_sha256":"7b31ebcd028d887637c68beb0288a3b57621f978bae21a5f8ffa15b7d769e552","abstract_canon_sha256":"81ca39d6a403c0378d2968dcd4f75c0b0ec4c8e848655c159ace093181b78e80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:24.795440Z","signature_b64":"qQLrd/7vEg8+aOjcvPExrKlOtvUc/5l7wCiuLcv+fAlxWSWnvc22t364VfjXNpdMp6f7Gx2LaIfvcLMKhMuBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51857b55caaab916c882c151fbc4e2c21c8d287d52171c1fc3e8123f407c5360","last_reissued_at":"2026-05-18T00:03:24.794762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:24.794762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exceptional poles of local $L$-functions for $GSp(4)$ with respect to split Bessel models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rainer Weissauer","submitted_at":"2017-12-18T12:37:46Z","abstract_excerpt":"Piateskii-Shapiro defined local $L$-factors $L^{PS}(s,\\Pi,\\Lambda)$ attached to irreducible admissible representations $\\Pi$ of the group $GSp(4)$ over local fields and Bessel models of $\\Pi$ attached to Bessel data $\\Lambda$. 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