{"paper":{"title":"On the structure of order 4 class groups of $\\mathbb{Q}(\\sqrt{n^2+1})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Azizul Hoque, Kalyan Chakraborty, Mohit Mishra","submitted_at":"2019-02-14T07:37:17Z","abstract_excerpt":"Groups of order $4$ are isomorphic to either $\\mathbb{Z}/4\\mathbb{Z}$ or $\\mathbb{Z}/2\\mathbb{Z} \\times \\mathbb{Z}/2\\mathbb{Z}$. We give certain sufficient conditions permitting to specify the structure of class groups of order $4$ in the family of real quadratic fields $\\mathbb{Q}{(\\sqrt{n^2+1})}$ as $n$ varies over positive integers. Further, we compute the values of Dedekind zeta function attached to these quadratic fields at the point $-1$. As a side result, we show that the size of the class group of this family could be made as large as possible by increasing the size of the number of di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05250","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.05250/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"}