{"paper":{"title":"On extremal properties of Jacobian elliptic functions with complex modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Franti\\v{s}ek \\v{S}tampach, Petr Siegl","submitted_at":"2015-12-18T19:50:03Z","abstract_excerpt":"A thorough analysis of values of the function $m\\mapsto\\mbox{sn}(K(m)u\\mid m)$ for complex parameter $m$ and $u\\in (0,1)$ is given. First, it is proved that the absolute value of this function never exceeds 1 if $m$ does not belong to the region in $\\mathbb{C}$ determined by inequalities $|z-1|<1$ and $|z|>1$. The global maximum of the function under investigation is shown to be always located in this region. More precisely, it is proved that, if $u\\leq1/2$, then the global maxim is located at $m=1$ with the value equal to $1$. While if $u>1/2$, then the global maximum is located in the interv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06089","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"}