Law of inertia for the factorization of cubic polynomials - the case of primes 2 and 3
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Mathematica Slovaca |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.degruyter.com/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml |
| Doi | http://dx.doi.org/10.1515/ms-2016-0248 |
| Field | General mathematics |
| Keywords | cubic polynomial; type of factorization; discriminant |
| Description | Let D be an integer and let C_D be the set of all monic cubic polynomials x^3 + ax^2 + bx + c with integral coefficients and with the discriminant equal to D. Along the line of our preceding papers, the following Theorem has been proved: If D is square-free and 3 does not divide the class number of Q((-3D)^(1/2)), then all polynomials in C_D have the same type of factorization over the Galois field F_p where p is a prime, p > 3. In this paper, we prove the validity of the above implication also for primes 2 and 3. |
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