{"paper":{"title":"Finite Order Transcendental Entire Solutions of Coupled Fermat-Type Difference Equations in Several Complex Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Abhijit Banerjee, Jhilik Banerjee","submitted_at":"2026-06-27T04:12:21Z","abstract_excerpt":"Motivated by recent developments in complex difference equations and Nevanlinna theory in several complex variables, we investigate finite-order transcendental entire solutions of the coupled Fermat-type difference system: \\beas \\begin{cases} f_1^{n_1}(z)+ f_2^{m_1} \\left(z+c \\right) = 1,\\\\ f_2^{n_2}(z) + f_1^{m_2} \\left(z+c\\right) = 1, \\end{cases} \\eeas where $z,c=(c_1,c_2,\\ldots,c_n) \\in \\mathbb{C}^n$ for various choices of $n_i,m_i$, $i=1,2$. where $n_i,m_i\\in\\mathbb N$ and $n_i+m_i\\ge2$ $(i=1,2)$. Extending the classical investigations of Gross--Yang, Liu, Liu--Cao--Cao and more recently, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30683","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/2606.30683/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"}