{"paper":{"title":"On Determinants of Laplacians on Compact Riemann Surfaces Equipped with Pullbacks of Conical Metrics by Meromorphic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Victor Kalvin","submitted_at":"2017-12-15T00:11:05Z","abstract_excerpt":"Let $\\mathsf m$ be any conical (or smooth) metric of finite volume on the Riemann sphere $\\Bbb CP^1$. On a compact Riemann surface $X$ of genus $g$ consider a meromorphic funciton $f: X\\to {\\Bbb C}P^1$ such that all poles and critical points of $f$ are simple and no critical value of $f$ coincides with a conical singularity of $\\mathsf m$ or $\\{\\infty\\}$. The pullback $f^*\\mathsf m$ of $\\mathsf m$ under $f$ has conical singularities of angles $4\\pi$ at the critical points of $f$ and other conical singularities that are the preimages of those of $\\mathsf m$. We study the $\\zeta$-regularized det"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05405","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"}