{"paper":{"title":"Zeta functions for tensor products of locally coprime integral adjacency algebras of association schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Allen Herman, Mitsugu Hirasaka, Semin Oh","submitted_at":"2015-08-28T17:34:00Z","abstract_excerpt":"The zeta function of an integral lattice $\\Lambda$ is the generating function $\\zeta_{\\Lambda}(s) = \\sum\\limits_{n=0}^{\\infty} a_n n^{-s}$, whose coefficients count the number of left ideals of $\\Lambda$ of index $n$. We derive a formula for the zeta function of $\\Lambda_1 \\otimes \\Lambda_2$, where $\\Lambda_1$ and $\\Lambda_2$ are $\\mathbb{Z}$-orders contained in finite-dimensional semisimple $\\mathbb{Q}$-algebras that satisfy a \"locally coprime\" condition. We apply the formula obtained above to $\\mathbb{Z}S \\otimes \\mathbb{Z}T$ and obtain the zeta function of the adjacency algebra of the direc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07287","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"}