{"paper":{"title":"On the Hurwitz Zeta Function of Imaginary Second Argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Guglielmo Fucci","submitted_at":"2011-05-27T18:34:15Z","abstract_excerpt":"In this work we exploit Jonqui\\`{e}re's formula relating the Hurwitz zeta function to a linear combination of polylogarithmic functions in order to evaluate the real and imaginary part of $\\zeta_{H}(s,ia)$ and its first derivative with respect to the first argument $s$. In particular, we obtain expressions for the real and imaginary party of $\\zeta_{H}(s,i a)$ and its derivative for $s=m$ with $m\\in\\mathbb{Z}\\backslash\\{1\\}$ involving simpler transcendental functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5624","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"}