{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4WOF3JPLRDRIJNKXKIKFKNFM7N","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":"7f6993a385b64b13b29598629cba1318a137547dc403b0e3ef070ad65dffc3a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-02-20T00:57:27Z","title_canon_sha256":"5f5f20b12f0fb39d61f7fb79da931fc1be8326053ea37c781f11db2046f16b13"},"schema_version":"1.0","source":{"id":"1702.05827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05827","created_at":"2026-05-18T00:50:25Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05827v1","created_at":"2026-05-18T00:50:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05827","created_at":"2026-05-18T00:50:25Z"},{"alias_kind":"pith_short_12","alias_value":"4WOF3JPLRDRI","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4WOF3JPLRDRIJNKX","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4WOF3JPL","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:1d66c46464c05c611912e265af3c0f0799e6a08b24f2d54291e95eb402736391","target":"graph","created_at":"2026-05-18T00:50:25Z","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 show that there is an absolute constant $c > 1/2$ such that the Mahler measure of the Fekete polynomials $f_p$ of the form $$f_p(z) := \\sum_{k=1}^{p-1}{\\left( \\frac kp \\right)z^k}\\,,$$ (where the coefficients are the usual Legendre symbols) is at least $c\\sqrt{p}$ for all sufficiently large primes $p$. This improves the lower bound $\\left(\\frac 12 - \\varepsilon\\right)\\sqrt{p}$ known before for the Mahler measure of the Fekete polynomials $f_p$ for all sufficiently large primes $p \\geq c_{\\varepsilon}$. Our approach is based on the study of the zeros of the Fekete polynomials on the unit cir","authors_text":"Tam\\'as Erd\\'elyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-02-20T00:57:27Z","title":"Improved lower bounds for the Mahler measure of the Fekete polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05827","kind":"arxiv","version":1},"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:ba7f23082c51bb3abf8091afe7fc162deac47ccfbdc93742103e82bcd8d58b08","target":"record","created_at":"2026-05-18T00:50:25Z","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":"7f6993a385b64b13b29598629cba1318a137547dc403b0e3ef070ad65dffc3a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-02-20T00:57:27Z","title_canon_sha256":"5f5f20b12f0fb39d61f7fb79da931fc1be8326053ea37c781f11db2046f16b13"},"schema_version":"1.0","source":{"id":"1702.05827","kind":"arxiv","version":1}},"canonical_sha256":"e59c5da5eb88e284b55752145534acfb5603ad26862392930e7cc9d434686e75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e59c5da5eb88e284b55752145534acfb5603ad26862392930e7cc9d434686e75","first_computed_at":"2026-05-18T00:50:25.210612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:25.210612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qa7oUabEVM2jK0El97D39B0MtCxz8qEFFqt0+DkyfTNxZZnhn5wH9MCSvptogyDYw851bUM/l50gnk+ksz83Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:25.211360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba7f23082c51bb3abf8091afe7fc162deac47ccfbdc93742103e82bcd8d58b08","sha256:1d66c46464c05c611912e265af3c0f0799e6a08b24f2d54291e95eb402736391"],"state_sha256":"6e23634fefd4cf4d1b9a251e6c59eac1b3b5a68458ae09226ee746ed8d2b38b7"}