{"id":"W2320405581","doi":"10.1016/j.jnt.2006.10.004","title":"Evaluation of the convolution sums <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msub><mml:mo>∑</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>6</mml:mn><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> and <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si2.gif\" overflow=\"scroll\"><mml:msub><mml:mo>∑</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>l</mml:mi><mml:mo>+</mml:mo><mml:mn>3</mml:mn><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math>","year":2006,"lang":"lv","type":"article","venue":"Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":40,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"","keywords":"Scroll; Mathematics; Algorithm; Computer science; Engineering","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","metaepi_broad","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"consensus_categories":["metaepi_narrow","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"category_scores_codex":[0.02470721,0.01094938,0.004885263,0.008092648,0.01572102,0.01569506,0.02320945,0.02350852,0.3661325],"category_scores_gemma":[0.01921713,0.02084716,0.01968662,0.01380893,0.01893197,0.01383157,0.01922812,0.02036749,0.01489007],"about_ca_system_candidate":true,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006055003,"about_ca_system_score_gemma":0.01751791,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.01844063,"about_ca_topic_score_gemma":0.01652896,"domain_scores_codex":[0.909207,0.008693879,0.01937599,0.01624275,0.02488351,0.02159687],"domain_scores_gemma":[0.9271333,0.01669227,0.02361007,0.01577419,0.00402692,0.01276323],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.01449758,0.004067754,0.0001846415,0.007133959,0.01746105,0.008761594,0.007226018,0.0104272,0.007367916,0.4470539,0.4661368,0.009681566],"study_design_scores_gemma":[0.01793377,0.01188511,0.0001975407,0.01102974,0.02009479,0.01736255,0.01646936,0.01571296,0.8056964,0.05077539,0.01554946,0.01729288],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7283173,0.0138805,0.00352034,0.004145546,0.01898187,0.001071938,0.009422969,0.003520639,0.217139],"genre_scores_gemma":[0.9205539,0.01254379,0.007842776,0.006933642,0.01588243,0.01193956,0.01231522,0.01084798,0.001140745],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7983285,"threshold_uncertainty_score":0.9999615,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02394879045885574,"score_gpt":0.264800656817557,"score_spread":0.2408518663587013,"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."}}