The index of a quartic field defined by a trinomial X4 + aX + b
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Bibliographic record
Abstract
Consider an irreducible quartic polynomial of the form [Formula: see text], where [Formula: see text] satisfy [Formula: see text] or [Formula: see text], where [Formula: see text] denotes the exact power of a rational prime [Formula: see text] that divides an integer. Such a polynomial is called a [Formula: see text]-minimal quartic. Let [Formula: see text] be a field defined by a [Formula: see text]-minimal quartic. In this paper, we use [Formula: see text]-integral bases and introduce the concept of [Formula: see text]-index forms in order to determine the field index of [Formula: see text] via the coefficients of a defining polynomial in terms of certain congruence conditions.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| 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 | 0.000 | 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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