{"paper":{"title":"The Stokes phenomenon associated with the periodic zeta function $F(a,s)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris","submitted_at":"2014-07-10T13:41:24Z","abstract_excerpt":"The exponentially improved large-$a$ expansion for the Hurwitz zeta function $\\zeta(s,a)$ is exploited to examine the expansion of the periodic zeta function $F(a,s)$ in the upper half-plane of the variable $a$. It is shown that a double Stokes phenomenon takes place in the vicinity of the positive imaginary $a$-axis as $|a|\\ra\\infty$. This is a consequence of the fact that constituent parts of $F(a,s)$ involve two Hurwitz zeta functions resulting in two parallel Stokes lines at unit distance apart. Numerical calculations confirm the theoretical predictions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2782","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"}