Bibliographic record
Abstract
On Non-Vanishing of Certain L-Functions Shahab Shahabi Depar tment of Mathemat ics and Computer Science University of Lethbridge M. Sc. Thesis , 2003 This thesis presents the following: (i) A detailed exposition of Rankin's classical work on the convolution of two mod ular L-functions is given; (ii) Let S be the class of Dirichlet series with Euler product on Re(s) > 1 that can be continued analytically to Re(s) = 1 with a possible pole at s = 1. For F, G 6 G is non-vanishing on the line Re(s) = 1; (iii) Let TN be the set of newforms of weight 2 and level N. For / € TN, let L(sym 2 / , s) be the associated symmetric square L-function. Let So = cr0 + it0 with 1 — 0 and C S 0 ) £ is a constant depending only on s0 and e.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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 teacher head, 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".