{"paper":{"title":"Character analogues of certain Hardy-Berndt sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"M\\\"um\\\"un Can, Veli Kurt","submitted_at":"2015-06-05T11:18:16Z","abstract_excerpt":"In this paper we consider transformation formulas for \\[ B\\left( z,s:\\chi\\right) =\\sum\\limits_{m=1}^{\\infty}\\sum\\limits_{n=0} ^{\\infty}\\chi(m)\\chi(2n+1)\\left( 2n+1\\right) ^{s-1}e^{\\pi im(2n+1)z/k}. \\] We derive reciprocity theorems for the sums arising in these transformation formulas and investigate certain properties of them. With the help of the character analogues of the Euler--Maclaurin summation formula we establish integral representations for the Hardy-Berndt character sums $s_{3,p}\\left( d,c:\\chi\\right) $ and $s_{4,p}\\left( d,c:\\chi\\right) $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01867","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"}