{"id":"W4387024139","doi":"10.4153/s0008414x23000548","title":"Shifted moments of the Riemann zeta function","year":2023,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada; National Science and Technology Council; National Center for Theoretical Sciences","keywords":"Riemann zeta function; Mathematics; Riemann hypothesis; Riemann Xi function; Conjecture; Particular values of Riemann zeta function; Arithmetic zeta function; Proof of the Euler product formula for the Riemann zeta function; Critical line; Z function; Pure mathematics; Explicit formulae; Function (biology); Mathematical analysis; Prime zeta function; Mathematical physics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001874621,0.0001237755,0.0003394041,0.0003520378,0.0001307893,0.00003386777,0.0006153799,0.00008008697,0.0003585583],"category_scores_gemma":[0.001995646,0.00008362691,0.0002128889,0.0007992321,0.0001707214,0.00009381997,0.00004643164,0.0002963564,0.00008404286],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001321582,"about_ca_system_score_gemma":0.0007475246,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001357408,"about_ca_topic_score_gemma":0.001853678,"domain_scores_codex":[0.9982147,0.0001108823,0.0006834652,0.00008039677,0.0005716615,0.0003388575],"domain_scores_gemma":[0.9978205,0.0005105809,0.0005327495,0.00045167,0.0003559517,0.0003285339],"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":[0.00004487576,0.0002655944,0.01191151,0.001657922,0.001302598,0.0002448383,0.01185746,0.00009453522,0.0008940206,0.7883928,0.1821478,0.001185965],"study_design_scores_gemma":[0.0004447526,0.00008513929,0.001953753,0.0003952454,0.0001914615,0.000109075,0.00291712,0.0007023995,0.0004877402,0.9902387,0.002348786,0.0001258433],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9878747,0.0000631142,0.002274347,0.001099637,0.0005264327,0.0002742877,0.00002607448,0.00001820109,0.007843162],"genre_scores_gemma":[0.9911259,0.000007685088,0.002474738,0.00005001374,0.0001185823,0.000002712596,0.000001146355,0.00004649169,0.006172686],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2018458,"threshold_uncertainty_score":0.3925962,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07896750856534289,"score_gpt":0.3180159946551869,"score_spread":0.239048486089844,"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."}}