{"id":"W1991650054","doi":"10.4153/cjm-2004-019-1","title":"Theta Series, Eisenstein Series and Poincaré Series over Function Fields","year":2004,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"National Science Foundation","keywords":"Poincaré series; Series (stratigraphy); Mathematics; Eisenstein series; Function series; Pure mathematics; Geometric series; Function (biology); Algebra over a field; Mathematical analysis; Power series; Modular form","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"],"consensus_categories":[],"category_scores_codex":[0.0004876622,0.0003029602,0.0006124175,0.0002599522,0.0002452028,0.0001928254,0.0002547581,0.0001826336,0.0002336853],"category_scores_gemma":[0.001179055,0.000259262,0.0001505241,0.0001871784,0.0003442377,0.001202473,0.00004381525,0.0003682354,0.00001601916],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000190713,"about_ca_system_score_gemma":0.0005801241,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001821914,"about_ca_topic_score_gemma":0.0138544,"domain_scores_codex":[0.9981542,0.00004015819,0.000857518,0.0001605209,0.0003566234,0.0004309497],"domain_scores_gemma":[0.9980812,0.0002041175,0.0005223451,0.0003813583,0.0002849498,0.0005260209],"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":[0.00003762341,0.00007025145,0.00007382537,0.0009030844,0.0001682268,0.0002682186,0.004316492,0.00005241181,0.0002509789,0.9911466,0.002584776,0.0001275375],"study_design_scores_gemma":[0.0005270132,0.0003820014,0.00007774636,0.0005127399,0.000174097,0.002574858,0.004637987,0.000007331623,0.001374126,0.9863649,0.003091515,0.0002756534],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9348345,0.002112464,0.03454548,0.00585527,0.001591303,0.0008166753,0.00008921295,0.0001438371,0.02001129],"genre_scores_gemma":[0.7803183,0.0003698112,0.1977867,0.0002610957,0.0006861312,0.00001676291,0.000005242947,0.0002134839,0.02034244],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1632412,"threshold_uncertainty_score":0.9999859,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02297877384854313,"score_gpt":0.2485205133572441,"score_spread":0.225541739508701,"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."}}