{"paper":{"title":"Silverman's conjecture for additive polynomial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vesselin Dimitrov","submitted_at":"2015-11-12T20:36:10Z","abstract_excerpt":"Let $F : \\mathrm{End}_{\\mathbb{F_p}}(\\mathbb{G}_{a/K}^d)$ be an additive polynomial mapping over a global function field $K/\\mathbb{F}_q$, and let $P \\in \\mathbb{G}_a^d(K)$. Following Silverman, consider $\\delta := \\lim_{n \\in \\mathbb{N}} (\\deg{F^{n}})^{1/n}$ the dynamic degree of $F$ and $\\alpha(P) := \\limsup_{n \\in \\mathbb{N}} h_K(F^{n}P)^{1/n}$ the arithmetic degree of $F$ at $P$. We have $\\alpha(P) \\leq \\delta$, and extending a conjecture of Silverman from the number field case, it is expected that equality holds if the orbit of $P$ is Zariski-dense.\n  We prove a weaker form of this conjec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04061","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}