{"paper":{"title":"On multiplicativity of Fourier coefficients at cusps other than infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Joseph Hundley","submitted_at":"2011-02-11T07:32:27Z","abstract_excerpt":"This paper treats the problem of determining conditions for the Fourier coefficients of a Maass-Hecke newform at cusps other than infinity to be multiplicative. To be precise, the Fourier coefficients are defined using a choice of matrix in SL(2, Z) which maps infinity to the cusp in question. Let c and d be the entries in the bottom row of this matrix, and let N be the level. In earlier work with Dorian Goldfeld and Min Lee, we proved that the coefficients will be multiplicative whenever N divides 2cd. This paper proves that they will not be multiplicative unless N divides 576cd. Further, if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2295","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"}