{"paper":{"title":"Transcendence degrees of fields generated by exponentials of products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Heinrich Massold","submitted_at":"2025-06-01T19:00:18Z","abstract_excerpt":"Let $\\theta=(\\theta_1,\\ldots,\\theta_m) \\in \\R^m, \\kappa=(\\kappa_1,\\ldots,\\kappa_n) \\in \\R^n$ be two tuples of real numbers each linearly independent over $\\Q$, and $T$ the transcendence degree of the field generated by $\\{\\exp(\\theta_i \\kappa_j) | i=1,\\ldots,m, \\; j=1,\\ldots,n \\}$ over $\\Q$. The estimate $T \\geq \\frac{mn}{m+n} -1$ has been conjectured for some time but could only be proved under additional hypotheses for $\\theta$ and $\\kappa$. This paper proves a weaker estimate for $T$ while also reducing the strong estimate to a prominent conjecture on intersections of subvarieties of split "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01123","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.01123/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}