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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.02700","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-01-12T16:30:31Z","cross_cats_sorted":[],"title_canon_sha256":"89e154780df46175fc4259f92ef64853aa5158012314cc52c9cd863233528f5c","abstract_canon_sha256":"4f8c506d0c4d4dba4409a059ff43ccf5c98b2a5b86467c69fe18f1ef48ca117f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:07.336579Z","signature_b64":"1u7G11AC7zJzr1YZFQq3lctqPweZAmD0cQ+NliVwxPdfMU5JUmzCYW9SoMmYlcHo0EJ7wY4DmJfiO9DPo0PxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2abaf07484fa5c569d19a2ca2ee74050dca6e9e5e230d0a9a6182247e447338a","last_reissued_at":"2026-05-18T01:16:07.335966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:07.335966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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