{"paper":{"title":"Twisters and signed fundamental domains for number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eduardo Friedman, Milton Espinoza","submitted_at":"2019-03-17T13:59:20Z","abstract_excerpt":"We give a signed fundamental domain for the action on $\\mathbb{R}^{r_1}_+\\times{\\mathbb{C}^*}^{r_2}$ of the totally positive units $E_+$ of a number field $k$ of degree $n=r_1+2r_2$ which we assume is not totally complex. Here $r_1$ and $r_2$ denote the number of real and complex places of $k$ and $\\mathbb{R}_+$ denotes the positive real numbers. The signed fundamental domain consists of $n$-dimensional $k$-rational cones $C_\\alpha$, each equipped with a sign $\\mu_\\alpha=\\pm1$, with the property that the net number of intersections of the cones with any $E_+$-orbit is 1.\n  The cones $C_\\alpha$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07089","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"}