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R \\leq \\phi(n,m) \\leq R+\\delta \\} \\lesssim \\max \\{R^{d-2+\\frac{2}{d+1}}, R^{d-1} \\delta \\}.$$\n  This is a variable coefficient version of a result proved by Lettington in \\cite{L10}, extending a previous result by Andrews in \\cite{A63}, showing that if $B \\subset {\\Bbb R}^d$, $d \\ge 2$, is a symmetric convex body with a "},"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":"1103.1670","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-09T00:15:17Z","cross_cats_sorted":["math.AP","math.CO","math.NT"],"title_canon_sha256":"ab28c4375bea8ba21026ad9da3bb17d209a1ce00127993816f2878f1cf8bd21f","abstract_canon_sha256":"78ed8e95fd9ae00aa91c300396c26f0509c466e33704cca9a1cf1dd19b805a96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:55.418055Z","signature_b64":"+jA/r8PJ3QCob3ozuoTObe2MonsUFv5C3bM7hs5+C4fFZk/fRN8xCfjWLhaEjNQRrB9TRRWA5YTph+rGEJmmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b51b2fc1016ae77de842c75651888360762c0fd05b515a3bf64c43819a4dee3","last_reissued_at":"2026-05-18T04:26:55.417608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:55.417608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattice points close to families of surfaces, non-isotropic dilations and regularity of generalized Radon transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CO","math.NT"],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Krystal Taylor","submitted_at":"2011-03-09T00:15:17Z","abstract_excerpt":"We prove that if $\\phi: {\\Bbb R}^d \\times {\\Bbb R}^d \\to {\\Bbb R}$, $d \\ge 2$, is a homogeneous function, smooth away from the origin and having non-zero Monge-Ampere determinant away from the origin, then $$ R^{-d} # \\{(n,m) \\in {\\Bbb Z}^d \\times {\\Bbb Z}^d: |n|, |m| \\leq CR; 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