{"paper":{"title":"Quadratic reciprocity and Some \"non-differentiable\" functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Azizul Hoque, Kalyan Chakraborty","submitted_at":"2017-10-21T09:18:59Z","abstract_excerpt":"Riemann's non-differentiable function and Gauss's quadratic reciprocity law have attracted the attention of many researchers. In \\cite{RM} Murty and Pacelli gave an instructive proof of the quadratic reciprocity via the theta-transformation formula and Gerver \\cite{G1} was the first to give a proof of differentiability/non-differentiability of Riemnan's function. The aim here is to survey some of the work done in these two questions and concentrates more onto a recent work of the first author along with Kanemitsu and Li \\cite{K1}. In that work \\cite{K1} an integrated form of the theta function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07777","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"}