Alberta Number Theory Days – L-functions
Bibliographic record
Abstract
fell at the very start of the newly formed PIMS CRG in Number Theory, and was thus an excellent opportunity to kickstart interactions between three of the participating institutions, the universities of Alberta, Calgary and Lethbridge. A broad range of topics in number theory were featured, but almost all talks were in areas motivated by the understanding of L-functions. Indeed, two key frameworks in which L-functions are viewed were addressed during the weekend, each forming a core of talks. The first framework is the analytic study of L-functions with the view to deriving properties of prime numbers. This included a reformulation of the generalized Riemann hypothesis by Brandon Fodden in terms of a decidable property of the natural numbers, thus giving a new insight into this most important of conjectures. In a related direction, Amir Akbary (discussing joint work with Brandon Fodden) gave improved bounds on the power moments of L-functions in the Selberg class, with applications to principal automorphic L-functions and Artin L-functions. Kaneenika Sinha’s presentation also concerned bounds, but this time bounds on the analytic rank of Jacobians of modular curves, an area of study with links to the famous conjecture of Birch and Swinnerton-Dyer. The second framework is the overarching Langlands programme, one of whose principal goals is to equate L-functions of Galois representations, important objects associated with the absolute Galois group of Q, with
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.004 | 0.003 |
| Scholarly communication | 0.006 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.080 | 0.021 |
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".