{"paper":{"title":"Remark on the roots of generalized Lens equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mutsuo Oka","submitted_at":"2017-06-09T05:59:26Z","abstract_excerpt":"We consider roots of a generalized Lens polynomial $L(z,\\bar z)={\\bar z}^m q(z)-p(z)$ and also harmonically splitting Lens type polynomial $L^{hs}(z,\\bar z)=r(\\bar z)q(z)-p(z)$ and with ${\\rm deg}\\,q(z)=n$, ${\\rm deg}\\,r(\\bar z)=m$ and ${\\rm deg}\\,p(z)\\le n$. We have shown that there exists a harmonically splitting polynomial $r(\\bar z)q(z)-p(z)$ which takes $5n+m-6$ roots, using a bifurcation family of polynomials. In this note, we show that this number can be taken by a generalized Lens polynomial ${\\bar z}^mq(z)-p(z)$ after a slight modification of the bifurcation family of a Rhie polynomia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02840","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"}