{"id":"W2950834864","doi":"10.48550/arxiv.1108.4980","title":"Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Ramanujan's sum; Elliptic integral; Jacobi elliptic functions; Elliptic function; Mathematics; Class (philosophy); Pure mathematics; Moduli; Series (stratigraphy); Lattice (music); Ramanujan tau function; Ramanujan theta function; Theta function; Quarter period; Algebra over a field; Mathematical analysis; Elliptic curve; Physics; 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":[],"consensus_categories":[],"category_scores_codex":[0.0003458343,0.0002672306,0.0003963855,0.0001445256,0.0002404099,0.00002657083,0.0003631078,0.0001530684,0.000374662],"category_scores_gemma":[0.0002658182,0.0002305516,0.0001720979,0.0001962208,0.0006217996,0.0002171953,0.000832469,0.0004149883,0.00005616775],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007185955,"about_ca_system_score_gemma":0.0000979149,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005880236,"about_ca_topic_score_gemma":0.0001208325,"domain_scores_codex":[0.9987504,0.0001475201,0.0003173306,0.0004371163,0.0001348258,0.0002128269],"domain_scores_gemma":[0.9977655,0.0006620073,0.0003627012,0.000830811,0.0002929409,0.00008596886],"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":[0.00004872148,0.0001830532,0.0001580479,0.0004154612,0.000277473,0.00001540155,0.0006921441,0.01805941,0.0002019166,0.9794712,0.0004401354,0.00003701099],"study_design_scores_gemma":[0.0002885025,0.00004033708,0.0001604577,0.0001414483,0.0006523843,0.00001293944,0.0006046847,0.01105094,0.0003226005,0.9864721,0.00002674648,0.000226875],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.853925,0.0001992153,0.1307299,0.000115217,0.0004799274,0.0009867572,0.00007145602,0.0001793661,0.01331322],"genre_scores_gemma":[0.9789255,0.00005079617,0.004362512,0.00001366434,0.00004897266,0.000005162189,0.00001262115,0.00003310685,0.01654772],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1263674,"threshold_uncertainty_score":0.9401621,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1439262627258976,"score_gpt":0.2514774679329805,"score_spread":0.1075512052070829,"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."}}