{"paper":{"title":"On the pullback of an arithmetic theta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Stephen Kudla, Tonghai Yang","submitted_at":"2011-06-23T14:11:50Z","abstract_excerpt":"In this paper, we consider the relation between the simplest types of arithmetic theta series, those associated to the cycles on the moduli space $\\Cal C$ of elliptic curves with CM by the ring of integers $\\OK$ in an imaginary quadratic field $\\kay$, on the one hand, and those associated to cycles on the arithmetic surface $\\M$ parametrizing 2-dimensional abelian varieties with an action of the maximal order $O_B$ in an indefinite quaternion algebra $B$ over $\\Q$, on the other. We show that the arithmetic degree of the pullback to $Cal C$ of the arithmetic theta function of weight 3/2 valued "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4732","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"}