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- Title
A new local-global principle for quadratic functional fields.
- Authors
Benyash-Krivets, V.; Platonov, V.
- Abstract
The article presents a new mathematical theorem for quadratic functional fields. It states that the proof of the theorem uses the properties of Jacobian curve. It mentions the possible methods that can be used to the problem of nontrivial units' existence and explains several mathematical equations that support the new theorem. It discusses three theorems which include one that suggests that the ring Df contains a nontrivial unit only if there is a constant C, one that suggests that the ring Df includes a fundamental unit u= α + β √f, and one that suggests that the ring Df for the polynomial f(x) = X4 + bx + c includes a fundamental unit of n degree. It offers a new proof of the first theorem using particular methods.
- Subjects
JACOBIAN matrices; NUMERICAL solutions to equations; ALGEBRAIC fields; POLYNOMIALS; FUNDAMENTAL theorem of algebra; QUADRATIC equations; MATHEMATICAL constants; MATHEMATICAL variables; EVIDENCE
- Publication
Doklady Mathematics, 2010, Vol 82, Issue 1, p531
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562410040083