{"paper":{"title":"Truncated versions of Dwork's lemma for exponentials of power series and $p$-divisibility of arithmetic functiens","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.GR","authors_text":"Christian Krattenthaler (Universit\\\"at Wien), Thomas W. M\\\"uller (Queen Mary, University of London)","submitted_at":"2014-12-22T15:07:18Z","abstract_excerpt":"(Dieudonn\\'e and) Dwork's lemma gives a necessary and sufficient condition for an exponential of a formal power series $S(z)$ with coefficients in $Q_p$ to have coefficients in $Z_p$. We establish theorems on the $p$-adic valuation of the coefficients of the exponential of $S(z)$, assuming weaker conditions on the coefficients of $S(z)$ than in Dwork's lemma. As applications, we provide several results concerning lower bounds on the $p$-adic valuation of the number of permutation representations of finitely generated groups. In particular, we give fairly tight lower bounds in the case of an ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7014","kind":"arxiv","version":2},"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"}