{"paper":{"title":"An integral approach to the Gardner-Fisher and untwisted Dowker sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carlos M. da Fonseca, M. Lawrence Glasser, Victor Kowalenko","submitted_at":"2016-03-11T17:41:07Z","abstract_excerpt":"We present a new and elegant integral approach to computing the Gardner-Fisher trigonometric power sum, which is given by $$ S_{m,v}=\\left(\\frac \\pi{2m}\\right)^{2v}\\sum_{k=1}^{m-1}\\cos^{-2v}\\left(\\frac{k\\pi}{2m}\\right)\\, ,\n$$ We present a new and elegant integral approach to computing the Gardner-Fisher trigonometric power sum, which is given by $$ S_{m,v}=\\left(\\frac \\pi{2m}\\right)^{2v}\\sum_{k=1}^{m-1}\\cos^{-2v}\\left(\\frac{k\\pi}{2m}\\right)\\, ,\n$$ where $m$ and $v$ are positive integers. This method not only confirms the results obtained earlier by an empirical method, but it is also much more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03700","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"}