{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FL2V6YKE2LFCFRCCMMJAE3YGUQ","short_pith_number":"pith:FL2V6YKE","schema_version":"1.0","canonical_sha256":"2af55f6144d2ca22c4426312026f06a421e07bd064e9ef2e64eb3f67f6cdf781","source":{"kind":"arxiv","id":"1710.06841","version":3},"attestation_state":"computed","paper":{"title":"On generalized Fourier Transforms for standard L-functions (with an appendix by Wen-Wei Li)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Freydoon Shahidi","submitted_at":"2017-10-18T17:48:16Z","abstract_excerpt":"Any generalization of the method of Godement-Jacquet on principal L-functions for GL(n) to other groups as perceived by Braverman-Kazhdan and Ngo requires a Fourier transform on a space of Schwartz functions. In the case of standard L-functions for classical groups, a theory of this nature was developed by Piatetski-Shapiro and Rallis, called the doubling method. It was later that Braverman and Kazhdan, using an algebro-geometric approach, different from doubling method, introduced a space of Schwartz functions and a Fourier transform, which projected onto those from doubling method. In both m"},"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":"1710.06841","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-18T17:48:16Z","cross_cats_sorted":[],"title_canon_sha256":"c545b0fd7c530299c7734648041490eadc627e4daa3f9f364f2e27ae7bc13460","abstract_canon_sha256":"a5fb0afa2b43f40b03548782bd6ff271c7c2d366f7c5f25e98babdccc1c1563b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:46.160242Z","signature_b64":"QWmocjNI4c2i2gwPbwz7Sjsj/Ft5GF5E3Ke5x1AmUK4YnEbufqO7AVDbZG+jJ7uyiKmvdWoZy0dxulCYmwSCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2af55f6144d2ca22c4426312026f06a421e07bd064e9ef2e64eb3f67f6cdf781","last_reissued_at":"2026-05-18T00:18:46.159484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:46.159484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On generalized Fourier Transforms for standard L-functions (with an appendix by Wen-Wei Li)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Freydoon Shahidi","submitted_at":"2017-10-18T17:48:16Z","abstract_excerpt":"Any generalization of the method of Godement-Jacquet on principal L-functions for GL(n) to other groups as perceived by Braverman-Kazhdan and Ngo requires a Fourier transform on a space of Schwartz functions. In the case of standard L-functions for classical groups, a theory of this nature was developed by Piatetski-Shapiro and Rallis, called the doubling method. It was later that Braverman and Kazhdan, using an algebro-geometric approach, different from doubling method, introduced a space of Schwartz functions and a Fourier transform, which projected onto those from doubling method. In both m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06841","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.06841","created_at":"2026-05-18T00:18:46.159606+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.06841v3","created_at":"2026-05-18T00:18:46.159606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06841","created_at":"2026-05-18T00:18:46.159606+00:00"},{"alias_kind":"pith_short_12","alias_value":"FL2V6YKE2LFC","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FL2V6YKE2LFCFRCC","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FL2V6YKE","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ","json":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ.json","graph_json":"https://pith.science/api/pith-number/FL2V6YKE2LFCFRCCMMJAE3YGUQ/graph.json","events_json":"https://pith.science/api/pith-number/FL2V6YKE2LFCFRCCMMJAE3YGUQ/events.json","paper":"https://pith.science/paper/FL2V6YKE"},"agent_actions":{"view_html":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ","download_json":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ.json","view_paper":"https://pith.science/paper/FL2V6YKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.06841&json=true","fetch_graph":"https://pith.science/api/pith-number/FL2V6YKE2LFCFRCCMMJAE3YGUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/FL2V6YKE2LFCFRCCMMJAE3YGUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/action/storage_attestation","attest_author":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/action/author_attestation","sign_citation":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/action/citation_signature","submit_replication":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/action/replication_record"}},"created_at":"2026-05-18T00:18:46.159606+00:00","updated_at":"2026-05-18T00:18:46.159606+00:00"}