{"paper":{"title":"Inverse Logarithmic Coefficients, Differences, Hankel Determinant, and Fekete--Szeg\\\"{o} Functionals for the Class $\\mathcal{C}_e$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nabadwip Sarkar, Pradip Das","submitted_at":"2026-05-19T09:55:12Z","abstract_excerpt":"In this paper, we investigate the inverse logarithmic coefficients associated with the class $\\mathcal{C}_e$ of analytic and univalent functions satisfying the subordination condition \\[ 1+\\frac{z f''(z)}{f'(z)} \\prec e^z, \\quad z\\in\\mathbb{D}. \\] If $F_{f^{-1}}(w) = \\log\\!\\left(\\frac{f^{-1}(w)}{w}\\right) = 2\\sum_{n=1}^{\\infty}\\Gamma_n w^n$ denotes the logarithmic expansion corresponding to the inverse function $f^{-1}$, then we establish sharp estimates for the initial inverse logarithmic coefficients and prove that \\[ |\\Gamma_n| \\le \\frac{1}{2n(n+1)}, \\qquad n=1,2,3. \\] We further derive the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19614","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19614/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}