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In this paper we prove for a $p$-group $G$ with exponent $\\exp(G)=q$ the upper bound $s_{kq}(G)\\le(k+2d-2)q+3D(G)-3$ whenever $k\\geq d$, where $d=\\Big\\lceil\\frac{D(G)}{q}\\Big\\rceil$ and $p$ is a prime s"},"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":"1503.06905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-24T03:54:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"dd5becbefb1f4e05509fbd638e1280e2bb912d94bccafad138ed6985be9b45d1","abstract_canon_sha256":"e68167d4e49a454f01295c271cff8944b2bf47fb9b5511e3460ef66c02e05ca1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:08.616516Z","signature_b64":"Su9t2mKJIICQpCYxA/hsNUrj+LtNvmp6PgHhX487hSJXOFmAvlr8zpaoZRQqflDDfWZFfh5tWkod+UTsMd7gBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee6da113614174d727fc52f118d13d57936331ee73950d26f2b49a009550064c","last_reissued_at":"2026-05-18T00:40:08.615985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:08.615985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zero-sum Subsequences of Length kq over Finite Abelian p-Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Xiaoyu He","submitted_at":"2015-03-24T03:54:18Z","abstract_excerpt":"For a finite abelian group $G$ and a positive integer $k$, let $s_{k}(G)$ denote the smallest integer $\\ell\\in\\mathbb{N}$ such that any sequence $S$ of elements of $G$ of length $|S|\\geq\\ell$ has a zero-sum subsequence with length $k$. 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