{"id":"W4396815993","doi":"10.48550/arxiv.2405.04698","title":"A note on Fourier coefficients of Hecke eigenforms in short intervals","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Division of Mathematical Sciences; Queen's University","keywords":"Mathematics; Fourier series; Fourier transform; Mathematical analysis","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":[0.0005845203,0.0004230647,0.0007648793,0.0003961002,0.00003009374,0.00003154213,0.0008558978,0.0003560224,0.0001440816],"category_scores_gemma":[0.0003141006,0.0004059462,0.0004350979,0.0005866672,0.0001988189,0.00006060188,0.001254655,0.001098388,0.0002278107],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004092381,"about_ca_system_score_gemma":0.0001039056,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002330829,"about_ca_topic_score_gemma":0.00002918538,"domain_scores_codex":[0.9980631,0.0001013941,0.000528931,0.0007199959,0.0002055928,0.0003809815],"domain_scores_gemma":[0.9979081,0.0005865355,0.0001481971,0.001145455,0.00009680988,0.0001148821],"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":[0.0001213264,0.0005721617,0.00009951145,0.001323642,0.0001495446,0.0002175597,0.00102551,0.01091057,0.00008872564,0.9849659,0.0002159437,0.0003096529],"study_design_scores_gemma":[0.0002362912,0.00009299029,0.00003900451,0.001377898,0.0001596685,0.00000128799,0.0001520629,0.05034969,0.002139306,0.9450579,0.0000310433,0.0003628884],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9480693,0.00001272389,0.02020774,0.00002442694,0.0004293748,0.0006354981,0.00006158431,0.0001393383,0.03042003],"genre_scores_gemma":[0.9976389,0.00001717347,0.000993426,0.00003149781,0.00006200392,0.000002313083,0.00000823066,0.00006758147,0.001178863],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04956963,"threshold_uncertainty_score":0.9998392,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.129235650994172,"score_gpt":0.2755245120636049,"score_spread":0.1462888610694329,"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."}}