{"paper":{"title":"Quantitative equidistribution for the solutions of systems of sparse polynomial equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CV","authors_text":"Andr\\'e Galligo, Carlos D'Andrea, Mart\\'in Sombra","submitted_at":"2012-03-08T16:32:26Z","abstract_excerpt":"For a system of Laurent polynomials f_1,..., f_n \\in C[x_1^{\\pm1},..., x_n^{\\pm1}] whose coefficients are not too big with respect to its directional resultants, we show that the solutions in the algebraic n-th dimensional complex torus of the system of equations f_1=\\dots=f_n=0, are approximately equidistributed near the unit polycircle. This generalizes to the multivariate case a classical result due to Erdos and Turan on the distribution of the arguments of the roots of a univariate polynomial. We apply this result to bound the number of real roots of a system of Laurent polynomials, and to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1843","kind":"arxiv","version":3},"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"}