Bibliographic record
Abstract
Gross and Zagier were able to prove a relation between special values of derivatives of L-functions and algebro-geometrical data such as Heegner points and intersection numbers. A program initiated by Kudla generalized this to higher-dimensional cases and this has been a fruitful program of research for years. Here we prove two results in this direction. First, we consider the Shimura variety parametrizing pairs of CM abelian varieties of the same dimension with the same CM-field $K$ acting on them and define special cycles on this variety (over the integral model considered as a Deligne-Mumford stack) and relate the Arakelov degree of these special cycles to Fourier coefficients of totally positive index of Hilbert Eisenstein series. Then, we define Green functions on this Shimura variety and relate the degrees of Green functions to the Fourier coefficients of the same Eisenstein series with indices that are not totally positive (or the constant coefficient). In our second result, we do the same for the moduli space of pairs of abelian varieties first of which have CM by ring of integers $O_{K_0}$ of a CM-field $K_0$ and the second one is higher-dimensional and has an action by $O_{K_0}$. Then we use the same methods as in the first result to prove that the degrees of special cycles on this Shimura variety is related to Fourier coefficients of Eisenstein series.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".