{"id":"W2969288576","doi":"10.1007/s00209-021-02784-w","title":"A reduction principle for Fourier coefficients of automorphic forms","year":2021,"lang":"en","type":"preprint","venue":"Mathematische Zeitschrift","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Banff International Research Station for Mathematical Innovation and Discovery; Vetenskapsrådet; Göteborgs Universitet; Knut och Alice Wallenbergs Stiftelse; National Science Foundation","keywords":"Mathematics; Fourier series; Fourier transform; Pure mathematics; Automorphic form; Quotient; Unipotent; Fourier analysis; Reduction (mathematics); Mathematical analysis; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0009786626,0.0006008781,0.001353101,0.0003120176,0.0001565907,0.00009159811,0.0005956141,0.000665538,0.0002656137],"category_scores_gemma":[0.001762515,0.0005348356,0.0006382312,0.0003833427,0.0001329245,0.0001852013,0.0009184749,0.000697648,0.00001759998],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002185975,"about_ca_system_score_gemma":0.0002943948,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000281257,"about_ca_topic_score_gemma":0.000004582716,"domain_scores_codex":[0.9965071,0.00007583602,0.001275687,0.0008429432,0.0007192367,0.0005792184],"domain_scores_gemma":[0.9959587,0.000482811,0.001253582,0.001551484,0.0005992763,0.0001540939],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001091752,0.001600948,0.00006961012,0.01685663,0.0008645052,0.00001638714,0.003599631,0.0007439624,0.004639638,0.9626836,0.002722763,0.006093152],"study_design_scores_gemma":[0.003794216,0.000401311,0.0001603834,0.006423178,0.001401788,0.0002113232,0.002000647,0.01237287,0.1179677,0.8325728,0.02011798,0.002575839],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5143028,0.0005966624,0.4772889,0.0001176277,0.0009201899,0.002256916,0.0002660445,0.0002684245,0.003982352],"genre_scores_gemma":[0.6947754,0.00004233365,0.3016596,0.00002319374,0.0002573364,0.0006202718,0.000278029,0.0001868683,0.002156965],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1804725,"threshold_uncertainty_score":0.9997103,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05156938118696287,"score_gpt":0.3508850442105995,"score_spread":0.2993156630236367,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}