Bibliographic record
Abstract
The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the p-adic L-function of a modular form. In this thesis, we develop the theory of overconvergent modular symbols over a completely general number field and use it to construct p-adic L-functions for automorphic forms for GL2. In particular, we prove control theorems that say that the natural specialisation map from overconvergent to classical modular symbols is an isomorphism on the small slope subspaces, hence attaching a unique overconvergent modular symbol to a small slope cuspidal automorphic eigenform .Φ. From this overconvergent symbol we then obtain a p-adic distribution that interpolates certain critical L-values of .Φ. \nThe text is comprised of two largely independent parts. In the first, we develop the theory in concrete detail over imaginary quadratic fields, and in the process present a constructive definition of the p-adic L-function in this setting. In the second, which was joint work with Daniel Barrera Salazar (Université de Montréal), we provide an analogous theory over general number fields, though not in the same explicit detail. \n
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How this classification was reachedexpand
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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.014 | 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; both teacher heads agree on what is shown here.
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".