{"paper":{"title":"Monic integer Chebyshev problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. G. Pinner, I. E. Pritsker, P. B. Borwein","submitted_at":"2013-07-20T01:41:24Z","abstract_excerpt":"We study the problem of minimizing the supremum norm by monic polynomials with integer coefficients. Let ${\\M}_n({\\Z})$ denote the monic polynomials of degree $n$ with integer coefficients. A {\\it monic integer Chebyshev polynomial} $M_n \\in {\\M}_n({\\Z})$ satisfies $$ \\| M_n \\|_{E} = \\inf_{P_n \\in{\\M}_n ({\\Z})} \\| P_n \\|_{E}. $$ and the {\\it monic integer Chebyshev constant} is then defined by $$ t_M(E) := \\lim_{n \\rightarrow \\infty} \\| M_n \\|_{E}^{1/n}. $$ This is the obvious analogue of the more usual {\\it integer Chebyshev constant} that has been much studied.\n  We compute $t_M(E)$ for vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5362","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"}