Subconvexity for a double Dirichlet series and non-vanishing of L-functions
Bibliographic record
Abstract
We study a double Dirichlet series of the form [Formula: see text], where [Formula: see text] and [Formula: see text] are quadratic Dirichlet characters with prime conductors [Formula: see text] and [Formula: see text] respectively. A functional equation group isomorphic to the dihedral group of order 6 continues the function meromorphically to [Formula: see text]. The developed theory is used to prove an upper bound for the smallest positive integer [Formula: see text] such that [Formula: see text] does not vanish. Additionally, a convexity bound at the central point is established to be [Formula: see text] and a subconvexity bound of [Formula: see text] is proven. An application of bounds at the central point to the non-vanishing problem is also discussed.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".