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In this paper we give a bound for \\[ N(f,F,B):=|\\{\\textbf{x}\\in\\mathbb{Z}^{n+1}:\\max_{0\\leq i\\leq n}|x_{i}|\\leq B,\\exists t\\in\\mathbb{Z}\\text{ such that }f(t)=F(\\textbf{x})\\}|, \\] To do this, we introduce a generalization of the Heath-Brown and Munshi's power sieve and we extend two results by Deligne and Katz on estimates for additive and multiplicative characters in many variables."},"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":"1811.10560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-26T18:06:07Z","cross_cats_sorted":[],"title_canon_sha256":"0aa521726b25f30f919107811503e4a9f7407437f1a194f9399102860a8ca0f0","abstract_canon_sha256":"0c796069f39dc092e4398dc04cc6b28ea9a42c183c5b8b518b69d85413d26a38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:56.412587Z","signature_b64":"WodGWud0ktegOfpTPJfGCImw9dfNsP3eyHcdyDEi6l3+2e7AxNRrK19VYvWgx1mjT5IKfJ4kFoYVOZAHCpyBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"293a18067ee1db147edd3d07fb3d5c3a8d691e4841a319d8c24993d4f8005503","last_reissued_at":"2026-05-17T23:43:56.411883Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:56.411883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Polynomial Sieve and Sums of Deligne Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dante Bonolis","submitted_at":"2018-11-26T18:06:07Z","abstract_excerpt":"Let $f\\in\\mathbb{Z}[T]$ be any polynomial of degree $d>1$ and $F\\in\\mathbb{Z}[X_{0},...,X_{n}]$ an irreducible homogeneous polynomial of degree $e>1$ such that the projective hypersurface $V(F)$ is smooth. 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