{"id":"W2604503215","doi":"10.1515/forum-2017-0222","title":"Large sums of Hecke eigenvalues of holomorphic cusp forms","year":2018,"lang":"en","type":"preprint","venue":"Forum Mathematicum","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Cusp form; Holomorphic function; Cusp (singularity); Mathematics; Modular form; Combinatorics; Lambda; Eigenvalues and eigenvectors; Riemann hypothesis; Type (biology); Mathematical analysis; Pure mathematics; Physics; Geometry; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003565826,0.0006199496,0.001991557,0.0004261231,0.0001097532,0.00004434718,0.001564223,0.000628379,0.001829182],"category_scores_gemma":[0.001893068,0.0004918374,0.0007646817,0.0003104339,0.0006174569,0.0001191709,0.002635948,0.000745449,0.0002699899],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000118177,"about_ca_system_score_gemma":0.0002921365,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002533213,"about_ca_topic_score_gemma":0.00003496737,"domain_scores_codex":[0.9948814,0.0002117652,0.001887195,0.0006273007,0.001404595,0.0009877313],"domain_scores_gemma":[0.9938676,0.0009676953,0.001807567,0.002479569,0.0006906814,0.0001868688],"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":[0.0001528235,0.001589438,0.001779453,0.02516945,0.001516776,0.00002545096,0.007409825,0.00000559795,0.0007505197,0.9318358,0.02963334,0.0001315427],"study_design_scores_gemma":[0.0005696163,0.0001920335,0.00003040029,0.002167993,0.0002975549,0.0000239434,0.002261762,0.002082647,0.02056583,0.9710789,0.0002827176,0.0004465457],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9081302,0.000353262,0.05198391,0.0002827044,0.0004341662,0.00239592,0.0007233565,0.0002377381,0.03545873],"genre_scores_gemma":[0.9736562,0.00004834287,0.02032433,0.00002663559,0.0001401099,0.0001255483,0.00006957209,0.0002061369,0.005403114],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06552599,"threshold_uncertainty_score":0.9997534,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0747439724006125,"score_gpt":0.3713331427594842,"score_spread":0.2965891703588717,"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."}}