{"paper":{"title":"Solutions of diophantine equations as periodic points of $p$-adic algebraic functions, III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick Morton","submitted_at":"2020-05-20T22:17:19Z","abstract_excerpt":"All the periodic points of a certain algebraic function related to the Rogers-Ramanujan continued fraction $r(\\tau)$ are determined. They turn out to be $0, \\frac{-1 \\pm \\sqrt{5}}{2}$, and the conjugates over $\\mathbb{Q}$ of the values $r(w_d/5)$, where $w_d$ is one of a specific set of algebraic integers, divisible by the square of a prime divisor of 5, in the field $K_d=\\mathbb{Q}(\\sqrt{-d})$, as $-d$ ranges over all negative quadratic discriminants for which $\\left(\\frac{-d}{5}\\right) = +1$. This yields new insights on class numbers of orders in the fields $K_d$. Conjecture 1 of Part I is p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.10377","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/2005.10377/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"}