{"paper":{"title":"Ruelle type L-functions versus determinants of Laplacians for torsion free abelian groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Masato Wakayama, Nobushige Kurokawa, Yoshinori Yamasaki","submitted_at":"2007-02-08T02:46:30Z","abstract_excerpt":"We study Ruelle's type zeta and $L$-functions for a torsion free abelian group $\\G$ of rank $\\n\\ge 2$ defined via an Euler product. It is shown that the imaginary axis is a natural boundary of this zeta function when $\\n=2,4$ and 8, and in particular, such a zeta function has no determinant expression. Thus, conversely, expressions like Euler's product for the determinant of the Laplacians of the torus $\\bR^{\\n}/\\G$ defined via zeta regularizations are investigated. Also, the limit behavior of an arithmetic function arising from the Ruelle type zeta function is observed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702209","kind":"arxiv","version":2},"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"}