{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002258016,0.001587197,0.00098616,0.001872431,0.0008607915,0.003194772,0.001805528,0.0009845791,0.06784023],"category_scores_gemma":[0.01192952,0.0003917528,0.001311805,0.001840477,0.0007108479,0.002602975,0.001492379,0.001180406,0.0235507],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00108653,"about_ca_system_score_gemma":0.002233041,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00373285,"about_ca_topic_score_gemma":0.004928122,"domain_scores_codex":[0.9970823,0.0002544289,0.0002175955,0.0004508533,0.00167894,0.0003158264],"domain_scores_gemma":[0.99437,0.001964831,0.000259494,0.0005392647,0.002660028,0.0002064385],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"not_applicable","study_design_scores_codex":[0.002068771,0.0006559766,0.007057382,0.001667128,0.0002255561,0.0004513783,0.0005204398,0.03530252,0.04696731,0.04051077,0.07982811,0.7847447],"study_design_scores_gemma":[0.000315563,0.00144366,0.01608592,0.0003874368,0.0003166938,0.001573745,0.001917544,0.5537603,0.1900226,0.03537384,0.1985105,0.0002920499],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.1274129,0.001378406,0.6977119,0.001133936,0.002179535,0.0006034523,0.01217705,0.04128254,0.1161202],"genre_scores_gemma":[0.2754341,0.0007688911,0.6022927,0.0002999005,0.0002529698,0.0006116248,0.0194901,0.008328066,0.09252165],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.9321598,"threshold_uncertainty_score":0.2269481,"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."}}