Lie Algebra Actions on Jacobi Forms and Vector-Valued Harmonic Maass Forms
Bibliographic record
Abstract
In their study, Alfes-Neumann, Funke, Mertens, and Rosu examined Rolen’s work on theta functions on H × Cg, where H is the upper-half plane, and its corresponding complete ζ-function [Rol16][ ANFMR23]. Using the complete ζ-function, they examined the vector-valued Eichler integral of newforms with integral Fourier coefficients and constructed Jacobi-Weierstrass mock modular forms that are weight-0 harmonic Maass forms with its shadow being weight-2 modular forms. In our study, we examine the action of lie Algebra elements of the full Jacobi group on smooth functions on the Jacobi group, specifically the lifts of smooth functions on H × Cg. We find elements of the complexified Lie algebra whose action on the lifts directly corresponds to differential operators that act on Jacobi forms to create Jacobi forms of the same index and different weights. Using these new Jacobi forms we create Jacobi forms of index 0 that are used to generalize the work of Alfes-Neumann, Funke, Mertens, and Rosu in creating vector-valued weight quotients which are harmonic Maass forms of weight 0 with the shadow being weight- 2 modular forms.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".