{"id":"W4401893936","doi":"10.3390/math12172624","title":"An Approximation of the Prime Counting Function and a New Representation of the Riemann Zeta Function","year":2024,"lang":"en","type":"article","venue":"Mathematics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Riemann zeta function; Riemann hypothesis; Logarithm; Analytic number theory; Prime number theorem; Chebyshev filter; Function (biology); Prime (order theory); Riemann Xi function; Representation (politics); Applied mathematics; Prime number; Pure mathematics; Discrete mathematics; Mathematical analysis; Combinatorics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001812695,0.0005828225,0.0005110925,0.001326756,0.0005788788,0.001752367,0.001441508,0.0009839376,0.002688115],"category_scores_gemma":[0.009093185,0.0002365092,0.000619898,0.0008581958,0.002518428,0.003917792,0.001347592,0.002422288,0.001084178],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009553504,"about_ca_system_score_gemma":0.0007923251,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008524691,"about_ca_topic_score_gemma":0.0004531349,"domain_scores_codex":[0.9993955,0.0001763549,0.00002024158,0.00009561758,0.0002455502,0.00006668527],"domain_scores_gemma":[0.9981291,0.0008578784,0.0001954599,0.0004238841,0.0002523228,0.0001413361],"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":[0.00004860687,0.00002296298,0.0005482096,0.00004592274,0.000005743302,0.00007338278,0.0001077599,0.02757744,0.004577061,0.9453357,0.001380538,0.02027671],"study_design_scores_gemma":[0.00001309592,0.00005005816,0.0004393926,0.0000346627,0.000008912057,0.0003390506,0.00004752637,0.566937,0.002949453,0.4193206,0.009826837,0.00003339975],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04834899,0.0008850112,0.9298504,0.00109489,0.0004147487,0.00002195932,0.00006121227,0.0002411931,0.01908162],"genre_scores_gemma":[0.6112747,0.001642688,0.3708098,0.0006558707,0.0006611916,0.00009944483,0.0001800823,0.000279434,0.01439672],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002688115,"threshold_uncertainty_score":0.009586573,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0763416913127584,"score_gpt":0.3467750442660527,"score_spread":0.2704333529532943,"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."}}