{"paper":{"title":"Congruences for Convolutions of Hilbert Modular Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Thomas Ward","submitted_at":"2012-01-20T17:08:34Z","abstract_excerpt":"Let $\\f$ be a primitive, cuspidal Hilbert modular form of parallel weight. We investigate the Rankin convolution $L$-values $L(\\f,\\g,s)$, where $\\g$ is a theta-lift modular form corresponding to a finite-order character. We prove weak forms of Kato's `false Tate curve' congruences for these values, of the form predicted by conjectures in non-commmutative Iwasawa theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4341","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"}