{"paper":{"title":"Higher residue symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Prem Prakash Pandey, R. Balasubramanian","submitted_at":"2011-03-01T09:16:42Z","abstract_excerpt":"Given a prime number $l$ and a finite set of integers $S=\\{a_1,...,a_m\\}$ we find out the exact degree of the extension $\\mathbb{Q}(a_1^{\\frac{1}{l}},...,a_m^{\\frac{1}{l}})/\\mathbb{Q}$. We give two different ways to compute this degree. The first method is using ramifiaction theory. The second proof follwos from our study of the distribution of primes $p$ for which all of $a_i$ are $l^{th}$ power residue simultaneously."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0110","kind":"arxiv","version":3},"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"}