{"paper":{"title":"An asymptotic formula for the zeros of the deformed exponential function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Cheng Zhang","submitted_at":"2015-01-12T16:30:31Z","abstract_excerpt":"We study the asymptotic representation for the zeros of the deformed exponential function $\\sum\\nolimits_{n = 0}^\\infty {\\frac1{n!}{q^{n(n - 1)/2}{x^n}}} $, $q\\in (0,1)$. Indeed, we obtain an asymptotic formula for these zeros: \\[x_n=- nq^{1-n}(1 + g(q)n^{-2}+o(n^{-2})),n\\ge1,\\] where $g(q)=\\sum\\nolimits_{k = 1}^\\infty {\\sigma (k){q^k}}$ is the generating function of the sum-of-divisors function $\\sigma(k)$. This improves earlier results by Langley and Liu. The proof of this formula is reduced to estimating the sum of an alternating series, where the Jacobi's triple product identity plays a ke"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02700","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"}