{"id":"W6979329577","doi":"","title":"Quadratic forms of holomorphic cusp forms and the decay of their $\\ell^p$-norms for $0 < p < 2$","year":2025,"lang":"en","type":"article","venue":"ArXiv.org","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Université de Montréal; National Natural Science Foundation of China; Centre de Recherches Mathématiques","keywords":"Holomorphic function; Cusp (singularity); Orthonormal basis; Bounded function; Hecke operator; Quadratic form (statistics); Modular form","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":[],"consensus_categories":[],"category_scores_codex":[0.001927169,0.0001983839,0.0006153079,0.0001285504,0.0001300834,0.000016696,0.0004790139,0.0001115183,0.000054523],"category_scores_gemma":[0.0007869824,0.0001012541,0.0002226098,0.0003458046,0.0007272004,0.000124152,0.0002087445,0.0001917591,0.000008572072],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003022745,"about_ca_system_score_gemma":0.0001091004,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000232304,"about_ca_topic_score_gemma":0.00006347623,"domain_scores_codex":[0.9984543,0.00008858319,0.0006321761,0.0002381971,0.000237659,0.0003490389],"domain_scores_gemma":[0.9959292,0.002812241,0.0002679641,0.000708522,0.0002232021,0.0000587998],"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":[0.0006784649,0.0002276489,0.08452868,0.001353367,0.0005188071,0.000001522876,0.002108458,0.000003083744,0.002482381,0.9058305,0.0007580681,0.001509014],"study_design_scores_gemma":[0.003537243,0.0001712831,0.004846225,0.0002332336,0.0001907333,0.000006971228,0.002593743,0.001016918,0.0537261,0.9331139,0.0003881565,0.0001754694],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9831222,0.0002712979,0.008899867,0.0008143185,0.00004708616,0.001019558,0.00002253969,0.00002675831,0.005776328],"genre_scores_gemma":[0.9962051,0.00006944524,0.0003438943,0.0000847642,0.00002067316,0.00009804006,0.00000469349,0.00002788404,0.003145484],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07968246,"threshold_uncertainty_score":0.4129021,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06694641094677625,"score_gpt":0.3455144229672187,"score_spread":0.2785680120204425,"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."}}