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Accessible Unlicensed Requires Authentication Published by De Gruyter February 28, 2017

Law of inertia for the factorization of cubic polynomials – the case of primes 2 and 3

Jiří Klaška and Ladislav Skula
From the journal Mathematica Slovaca

Abstract

Let D ∈ ℤ and let CD be the set of all monic cubic polynomials x3 + ax2 + bx + c ∈ ℤ[x] 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 ∤ h(−3D) where h(−3D) is the class number of Q(3D), then all polynomials in CD have the same type of factorization over the Galois field 𝔽p where p is a prime, p > 3. In this paper, we prove the validity of the above implication also for primes 2 and 3.


(Communicated by Stanislav Jakubec)


References

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[3] Klaška, J.—Skula, L.: Law of inertia for the factorization of cubic polynomials – the imaginary case, to appear in Util. Math.Search in Google Scholar

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Received: 2014-5-29
Accepted: 2015-5-14
Published Online: 2017-2-28
Published in Print: 2017-2-1

© 2017 Mathematical Institute Slovak Academy of Sciences