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Record W4388724733 · doi:10.1017/s0013091523000664

Generalized divisor functions in arithmetic progressions: II

2023· article· en· W4388724733 on OpenAlexaff
David T. Nguyen

Bibliographic record

VenueProceedings of the Edinburgh Mathematical Society · 2023
Typearticle
Languageen
FieldMathematics
TopicAnalytic Number Theory Research
Canadian institutionsQueen's University
FundersAmerican Institute of Mathematics
KeywordsDivisor (algebraic geometry)MathematicsArithmeticDivisor functionFunction (biology)Moment (physics)Algebra over a fieldDiscrete mathematicsPure mathematicsPhysics

Abstract

fetched live from OpenAlex

Abstract We obtain a new bound on the second moment of modified shifted convolutions of the generalized threefold divisor function and show that, for applications, the modified version is sufficient.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.003
metaresearch head score (Gemma)0.004
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.501
Threshold uncertainty score0.886

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.004
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.002
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0010.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.064
GPT teacher head0.349
Teacher spread0.284 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations0
Published2023
Admission routes1
Has abstractyes

Explore more

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