{"id":"W2050761221","doi":"10.1016/j.jmaa.2013.08.017","title":"The Dirichlet divisor problem, traces and determinants for complex powers of the twisted bi-Laplacian","year":2013,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Riemann zeta function; TRACE (psycholinguistics); Laplace operator; Divisor (algebraic geometry); Zeta function regularization; Pure mathematics; Function (biology); Heat kernel; Eigenvalues and eigenvectors; Laplacian matrix; Mathematical analysis; Dirichlet distribution; Semigroup; Dirichlet problem; Arithmetic zeta function; Prime zeta function; Boundary value problem; Physics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002477168,0.001380514,0.00189882,0.004721743,0.003018836,0.006933643,0.002357653,0.003020002,0.008389985],"category_scores_gemma":[0.008647006,0.0008298786,0.001137802,0.002332398,0.008008254,0.01069267,0.003864628,0.003680752,0.0009390501],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00207469,"about_ca_system_score_gemma":0.001624658,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001720066,"about_ca_topic_score_gemma":0.001570105,"domain_scores_codex":[0.9989135,0.000370374,0.00007347635,0.0001921175,0.0002695963,0.0001809147],"domain_scores_gemma":[0.997391,0.001026975,0.0002976168,0.0002542262,0.0002920773,0.0007380862],"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":[0.0000206986,0.00002471832,0.0001643787,0.00001989517,0.000004676716,0.0001077275,0.0001702244,0.0005685997,0.000329184,0.9968004,0.0004737782,0.001315618],"study_design_scores_gemma":[0.00001099186,0.000008296946,0.0001006813,0.00001222972,0.000003888575,0.0001040857,0.00009025154,0.008833929,0.0001276373,0.9900989,0.0005958093,0.00001330789],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7319711,0.003519979,0.1547477,0.008049943,0.001669413,0.00007055911,0.0002419702,0.0002531795,0.09947609],"genre_scores_gemma":[0.9530222,0.001369063,0.01186966,0.0005357066,0.001339686,0.00005754344,0.0002014677,0.0002038248,0.03140089],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008389985,"threshold_uncertainty_score":0.02806729,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03288912052777614,"score_gpt":0.3209518876408805,"score_spread":0.2880627671131043,"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."}}