{"id":"W2129660780","doi":"10.1142/s179304211000371x","title":"RAMANUJAN CONGRUENCES FOR SIEGEL MODULAR FORMS","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Ramanujan's sum; Congruence relation; Mathematics; Siegel modular form; Modular form; Pure mathematics; Modular design; Ramanujan theta function; Type (biology); Algebra over a field; Computer science","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007348993,0.0001068783,0.0001848453,0.0001045588,0.00004422148,0.00004785743,0.0005371469,0.00007039693,0.002928478],"category_scores_gemma":[0.001677262,0.00007894924,0.0002053533,0.0000498856,0.00008537705,0.0003580833,0.00004113342,0.0002743764,0.00004272018],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002528017,"about_ca_system_score_gemma":0.00004929263,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.664701e-7,"about_ca_topic_score_gemma":0.000005406976,"domain_scores_codex":[0.9989447,0.00002359537,0.0004129523,0.00009203806,0.0003829284,0.0001438103],"domain_scores_gemma":[0.9975154,0.001216756,0.000429364,0.0001205661,0.0006397078,0.00007814341],"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":[0.0002439143,0.0001560618,0.0007618975,0.00001408674,0.000286698,0.00003596267,0.0002467614,0.00001163012,0.003554959,0.97514,0.004693248,0.01485479],"study_design_scores_gemma":[0.0006880718,0.00003966906,0.0002808866,0.00003832668,0.00002441646,0.0003746072,0.0002273713,0.00004243247,0.00377375,0.9752996,0.01911127,0.00009959313],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9211943,0.00002391211,0.07051976,0.0005622185,0.002472057,0.0001050322,0.00008132371,0.00001885029,0.005022554],"genre_scores_gemma":[0.9727301,0.000007614136,0.02464621,0.0002576758,0.0009321183,0.000006508958,0.000007052797,0.00002009918,0.001392648],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05153579,"threshold_uncertainty_score":0.997983,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01816167492913321,"score_gpt":0.3594280317754529,"score_spread":0.3412663568463197,"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."}}