One‐level densities in families of Grössencharakters associated to CM elliptic curves
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract We study the low‐lying zeros of a family of ‐functions attached to the complex multiplication elliptic curve , for each odd and square‐free integer . Specifically, upon writing the ‐function of as for the appropriate Grössencharakter of conductor , we consider the collection of ‐functions attached to , , where for each integer , denotes the primitive character inducing . We observe that of the ‐functions in have negative root number. is thus not one of the essentially homogeneous families of the universality conjecture of Sarnak, Shin and Templier [33], with unitary, symplectic or orthogonal (odd or even) symmetry type. By computing the one‐level density in the family of ‐functions in with conductor at most , we find that naturally decomposes into subfamilies: more specifically, a collection of symplectic ( for , even) and orthogonal ( for , odd) subfamilies. For each such subfamily, we moreover compute explicit lower order terms in decreasing powers of .
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.
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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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