Law of inertia for the factorization of cubic polynomials – the case of primes 2 and 3
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Jiří Klaška
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
The second author was supported under Project P201/11/0276 of the Czech Science Foundation.
References
[1] Klaška, J.—Skula, L.: Mordell’s equation and the Tribonacci family, Fibonacci Quart. 49 (2011), 310–319.Search in Google Scholar
[2] Klaška, J.—Skula, L.: Law of inertia for the factorization of cubic polynomials – the real case, to appear in Util. Math.Search in Google Scholar
[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
[4] Klaška, J.—Skula, L.: Law of inertia for the factorization of cubic polynomials – the case of discriminants divisible by three, Math. Slovaca 66 (2016), 1019–1027.10.1515/ms-2015-0199Search in Google Scholar
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- State hoops
- On derivations of partially ordered sets
- Interior and closure operators on commutative basic algebras
- When is the cayley graph of a semigroup isomorphic to the cayley graph of a group
- Sequences of cantor type and their expressibility
- δ-Fibonacci and δ-lucas numbers, δ-fibonacci and δ-lucas polynomials
- Law of inertia for the factorization of cubic polynomials – the case of primes 2 and 3
- Closed hereditary coreflective subcategories in epireflective subcategories of Top
- Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments
- Difference of two strong Światkowski lower semicontinuous functions
- Fejér-type inequalities (II)
- Representation of maxitive measures: An overview
- On a conjecture of Y. H. Cao and X. B. Zhang
- On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces
- Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups
- Homological properties of banach modules over abstract segal algebras
- Variable Hajłasz-Sobolev spaces on compact metric spaces
- Commuting pairs of self-adjoint elements in C*-algebras
- Additivity of maps preserving products AP ± PA* on C*-algebras
- A note on derived connections from semi-symmetric metric connections
- Lindelöf P-spaces need not be Sokolov
- Strong convergence properties for arrays of rowwise negatively orthant dependent random variables
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