{"paper":{"title":"Transformation formulas of a character analogue of $\\log\\theta_{2}(z)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Merve \\c{C}elebi Bozta\\c{s}, M\\\"um\\\"un Can","submitted_at":"2017-10-13T16:49:16Z","abstract_excerpt":"In this paper, transformation formulas for the function \\[ A_{1}\\left(z,s:\\chi\\right)=\\sum\\limits_{n=1}^{\\infty}\\sum\\limits_{m=1}^{\\infty}\\chi\\left(n\\right)\\chi\\left(m\\right)\\left(-1\\right)^{m}n^{s-1}e^{2\\pi imnz/k} \\] are obtained. Sums that appear in transformation formulas are generalizations of the Hardy--Berndt sums $s_{j}(d,c),$ $j=1,2,5$. As applications of these transformation formulas, reciprocity formulas for these sums are derived and several series relations are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05001","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"}