Boundary Distributions for GL3 over a Local Field and Symmetric Power Coefficients
Bibliographic record
Abstract
In this thesis, we construct a residue map and a Poisson kernel between holomorphic discrete series representations on the Drinfeld period domain and harmonic cocycles with certain non-trivial coefficients on the Bruhat-Tits building for GL3 over a local field of any characteristic. In order to construct the Poisson kernel, we find a new locally analytic kernel function that can be integrated against general boundary distributions. Assuming the existence of certain boundary distributions attached to bounded harmonic \ncocycles, we prove that the Poisson kernel is a right inverse of the residue map for bounded harmonic cocycles. Moreover, we show that the existence of the needed boundary distributions follows from a non-criticality statement for a new class of automorphic forms. We prove a control theorem that implies this non-criticality statement for trivial coefficients. Finally, we apply our constructions to relate spaces of Drinfeld cusp forms for certain congruence subgroups of GL3 and spaces of harmonic cocycles extending work of Teitelbaum to GL3.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".