{"paper":{"title":"Sums of two squares in short intervals in polynomial rings over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Arno Fehm, Efrat Bank, Lior Bary-Soroker","submitted_at":"2015-09-07T12:44:02Z","abstract_excerpt":"Landau's theorem asserts that the asymptotic density of sums of two squares in the interval $1\\leq n\\leq x$ is $K/{\\sqrt{\\log x}}$, where $K$ is the Landau-Ramanujan constant. It is an old problem in number theory whether the asymptotic density remains the same in intervals $|n-x|\\leq x^{\\epsilon}$ for a fixed $\\epsilon$ and $x\\to \\infty$.\n  This work resolves a function field analogue of this problem, in the limit of a large finite field. More precisely, consider monic $f_0\\in \\mathbb{F}_q[T]$ of degree $n$ and take $\\epsilon$ with $1>\\epsilon\\geq \\frac2n$. Then the asymptotic density of poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02013","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":""},"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"}