{"paper":{"title":"Character sums to prime power moduli evaluated at binary quadratic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Short character sums to prime power moduli evaluated at binary quadratic forms admit explicit estimates.","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aishik Chattopadhyay, Stephan Baier","submitted_at":"2025-08-15T05:43:27Z","abstract_excerpt":"We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms. This complements estimates established by Heath-Brown for such character sums to squarefree moduli. Our approach uses $p$-adic analysis. More precisely, we use tools from the $p$-adic theory of exponential sums, as initiated by Mili\\'cevi\\'c."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The p-adic theory of exponential sums initiated by Milićević applies directly and without major additional restrictions to the evaluation at binary quadratic forms for prime power moduli.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives estimates for character sums to prime power moduli at binary quadratic forms, complementing Heath-Brown via p-adic methods initiated by Milićević.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Short character sums to prime power moduli evaluated at binary quadratic forms admit explicit estimates.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1b63366275f3473cfda85b5cf59da61dd717ee06cdfc62ac319bd3fbb4af3f1c"},"source":{"id":"2508.11231","kind":"arxiv","version":3},"verdict":{"id":"72688c78-a771-4db5-b862-af9c9454f781","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T23:19:58.603805Z","strongest_claim":"We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms.","one_line_summary":"Derives estimates for character sums to prime power moduli at binary quadratic forms, complementing Heath-Brown via p-adic methods initiated by Milićević.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The p-adic theory of exponential sums initiated by Milićević applies directly and without major additional restrictions to the evaluation at binary quadratic forms for prime power moduli.","pith_extraction_headline":"Short character sums to prime power moduli evaluated at binary quadratic forms admit explicit estimates."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.11231/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"8c36b8cb0f3d86700ce186f9bf234abea00fe9ff88dd7627f3c09d4e255c7ab2"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}