Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect
Bibliographic record
Abstract
This paper is an extension of Kim et al. (2020a), and we prove equidistribution theorems for families of holomorphic Siegel cusp forms of general degree in the level aspect.Our main contribution is to estimate unipotent contributions for general degree in the geometric side of Arthur's invariant trace formula in terms of Shintani zeta functions in a uniform way.Several applications, including the vertical Sato-Tate theorem and low-lying zeros for standard L-functions of holomorphic Siegel cusp forms, are discussed.We also show that the "nongenuine forms", which come from nontrivial endoscopic contributions by Langlands functoriality classified by Arthur, are negligible.1. Introduction 993 2. Preliminaries 998 3. Asymptotics of Hecke eigenvalues 1000 4. Arthur classification of Siegel modular forms 1010 5.A notion of newforms in S k ..N // 1017 6. Equidistribution theorem of Siegel cusp forms; proof of Theorem 1.1 1019 7. Vertical Sato-Tate theorem for Siegel modular forms: proofs of Theorems 1.2 and 1.3 1020 8. Standard L-functions of Sp.2n/ 1021 9. `-level density of standard L-functions 1024 10.The order of vanishing of standard L-functions at s D 1 2 1028
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".