Low-lying zeros of quadratic Dirichlet $L$-functions: A transition in\n the Ratios Conjecture
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Bibliographic record
Abstract
We study the $1$-level density of low-lying zeros of quadratic Dirichlet\n$L$-functions by applying the $L$-functions Ratios Conjecture. We observe a\ntransition in the main term as was predicted by the Katz-Sarnak heuristic as\nwell as in the lower order terms when the support of the Fourier transform of\nthe corresponding test function reaches the point $1$. Our results are\nconsistent with those obtained in previous work under GRH and are furthermore\nanalogous to results of Rudnick in the function field case.\n
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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