{"paper":{"title":"Signed fundamental domains for totally real number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eduardo Friedman, Francisco Diaz y Diaz","submitted_at":"2013-03-16T15:26:34Z","abstract_excerpt":"We give a signed fundamental domain for the action on $\\mathbb{R}^n_+$ of the totally positive units $E_+$ of a totally real number field $k$ of degree $n$. The domain $\\big\\{(C_\\sigma,w_\\sigma) \\big\\}_\\sigma$ is signed since the net number of its intersections with any $E_+$-orbit is 1, i. e. for any $x\\in \\mathbb{R}^n_+$, $$ \\sum_{\\sigma\\in S_{n-1}} \\sum_{\\varepsilon\\in E_+} w_\\sigma\\chi^{\\phantom{1}}_{C_\\sigma}(\\varepsilon x) = 1. $$ Here $\\chi_{C_\\sigma}$ is the characteristic function of $C_\\sigma$, $w_\\sigma=\\pm1$ is a natural orientation of the $n$-dimensional $k$-rational cone $C_\\sigm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3989","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"}