{"paper":{"title":"Weighted spectral large sieve inequalities for Hecke congruence subgroups of SL(2,Z[i])","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nigel Watt","submitted_at":"2013-02-13T14:53:18Z","abstract_excerpt":"We prove new bounds for weighted mean values of sums involving Fourier coefficients of cusp forms that are automorphic with respect to a Hecke congruence subgroup \\Gamma =\\Gamma_0(q) of the group SL(2,Z[i]), and correspond to exceptional eigenvalues of the Laplace operator on the space L^2(\\Gamma\\SL(2,C)/SU(2)). These results are, for certain applications, an effective substitute for the generalised Selberg eigenvalue conjecture. We give a proof of one such application, which is an upper bound for a sum of generalised Kloosterman sums (of significance in the study of certain mean values of Hec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3127","kind":"arxiv","version":3},"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"}