{"paper":{"title":"A Poincar\\'e series on hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Tathagata Basak","submitted_at":"2017-07-25T02:24:40Z","abstract_excerpt":"Let $L$ be the unique even self-dual lattice of signature $(25,1)$. The automorphism group $\\operatorname{Aut}(L)$ acts on the hyperbolic space $\\mathcal{H}^{25}$. We study a Poincar\\'e series $E(z,s)$ defined for $z$ in $\\mathcal{H}^{25}$, convergent for $\\operatorname{Re}(s) > 25$, invariant under $\\operatorname{Aut}(L)$ and having singularities along the mirrors of the reflection group of $L$. We compute the Fourier expansion of $E(z,s)$ at a \"Leech cusp\" and prove that it can be meromorphically continued to $\\operatorname{Re}(s) > 25/2$. Analytic continuation of Kloosterman sum zeta functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07790","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"}