{"id":"W65755943","doi":"10.1007/s10587-009-0052-0","title":"Evaluation of the sums % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaWaaabCaeaacqaHdpWCcqGGOaakcqWGTbqBcqGG % PaqkcqaHdpWCcqGGOaakcqWGUbGBcqGHsislcqWGTbqBcqGGPaqkaS % qaamaaxababaGaemyBa0Maeyypa0JaeGymaedameaacqWGTbqBcqGH % HjIUcqWGHbqycqGGOaakcyGGTbqBcqGGVbWBcqGGKbazcqaI0aancq % GGPaqkaeqaaaWcbaGaemOBa4MaeyOeI0IaeGymaedaniabggHiLdaa % aa!5C34! $$ \\sum\\limits_{\\mathop {m = 1}\\limits_{m \\equiv a(\\bmod 4)} }^{n - 1} {\\sigma (m)\\sigma (n - m)} $$","year":2009,"lang":"en","type":"article","venue":"Czechoslovak Mathematical Journal","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Combinatorics; Convolution (computer science); Sigma; Physics; Quantum mechanics","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":["metaresearch","metaepi_narrow","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"consensus_categories":["metaresearch","metaepi_narrow","sts","research_integrity","insufficient_payload"],"category_scores_codex":[0.03745107,0.006085871,0.008129766,0.003229069,0.004191039,0.002470677,0.01226575,0.004046959,0.00883304],"category_scores_gemma":[0.02469964,0.004911326,0.006204008,0.008269415,0.004497856,0.004409708,0.002907745,0.01231366,0.001738522],"about_ca_system_candidate":true,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004847642,"about_ca_system_score_gemma":0.005393379,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009540006,"about_ca_topic_score_gemma":0.0001151975,"domain_scores_codex":[0.9413538,0.009468711,0.0119314,0.005639166,0.02279633,0.008810586],"domain_scores_gemma":[0.9605573,0.006951652,0.007975645,0.01069925,0.009871385,0.003944717],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.004058327,0.02142176,0.003327546,0.004160668,0.01155821,0.002955944,0.01168037,0.003122705,0.03100971,0.3984078,0.4165418,0.09175515],"study_design_scores_gemma":[0.0201125,0.003175452,0.005493151,0.005180049,0.01160565,0.01168983,0.004599939,0.02488339,0.02384707,0.8513606,0.02906312,0.008989226],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6467355,0.008550705,0.04544034,0.0805583,0.009182843,0.02535047,0.001217197,0.005148562,0.1778161],"genre_scores_gemma":[0.9538466,0.0007745977,0.01925207,0.007778464,0.00485465,0.0006784902,0.0001595043,0.001740232,0.01091533],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4529528,"threshold_uncertainty_score":0.9990388,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09704370943723717,"score_gpt":0.3686180297891427,"score_spread":0.2715743203519055,"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."}}