Conjectures for Moments Associated With Cubic Twists of Elliptic Curves
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Bibliographic record
Abstract
We extend the heuristic introduced by Conrey, Farmer, Keating, Rubinstein, and Snaith in order to formulate conjectures for the (k,l)-moments of L-functions of elliptic curves twisted by cubic characters. We also apply the work of Keating and Snaith on the (k,l)-moments of characteristic polynomials of unitary matrices to extend our conjecture to k,l∈C such that Re(k),Re(l), and Re(k+l)>−1. Our conjectures are then numerically tested for two families. A novelty of our conjectures is that cubic twists naturally lead us to consider the possibility k=l.
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it