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Let $n\\in \\mathbb{N}$ be arbitrary, $\\mathbb{K}$ a field and $f_{1}, \\ldots, f_{n}\\colon \\mathbb{K}\\to \\mathbb{C}$ additive functions. Suppose further that equation \\[\n  \\sum_{i=1}^{n}f^{q_{i}}_{i}\\left(x^{p_{i}}\\right)=0\n  \\qquad\n  \\left(x\\in \\mathbb{K}\\right) \\] is also satisfied. Then the functions $f_{1}, \\ldots, f_{n}$ are linear combinations of field homomorphisms from $\\mathbb{K}$ to $\\mathbb{C}$."},"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":"1810.11999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-29T08:33:40Z","cross_cats_sorted":[],"title_canon_sha256":"810d4dc2dd63e472d9f618b48427434c8aa8caa058c9899c66ebd8e93aaffa32","abstract_canon_sha256":"908751f4bf60f49bd94b580d52386c0ddb19fb97bab59a4513bb20fa21dfe002"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:06.734580Z","signature_b64":"7WaPZrLJ3KHG+tb5aEc7YPptjv+ianUe5OY6dRZNFXyVgbOGrV2kGsVFrm+Q1ADoEFKQ5xNtkNk5NzAAN0j1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"702821ee50ebec0f4cebde378a9fbcef35254648ca4a448a725e3d0783e8c9d4","last_reissued_at":"2026-05-18T00:02:06.733927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:06.733927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization of field homomorphisms through Pexiderized functional equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Csaba Vincze, Eszter Gselmann, Gergely Kiss","submitted_at":"2018-10-29T08:33:40Z","abstract_excerpt":"The aim of this paper is to prove characterization theorems for field homomorphisms. More precisely, the main result investigates the following problem. Let $n\\in \\mathbb{N}$ be arbitrary, $\\mathbb{K}$ a field and $f_{1}, \\ldots, f_{n}\\colon \\mathbb{K}\\to \\mathbb{C}$ additive functions. Suppose further that equation \\[\n  \\sum_{i=1}^{n}f^{q_{i}}_{i}\\left(x^{p_{i}}\\right)=0\n  \\qquad\n  \\left(x\\in \\mathbb{K}\\right) \\] is also satisfied. 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