Relevant bibliographies by topics / Sextic Equations

Contents

  1. Journal articles

Academic literature on the topic 'Sextic Equations'

Author: Grafiati
Published: 29 July 2024
Last updated: 30 July 2024

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Sextic Equations.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Sextic Equations"

1

Gaál, István, Borka Jadrijević, and László Remete. "Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields." International Journal of Number Theory 15, no. 01 (2019): 11–27. http://dx.doi.org/10.1142/s1793042118501695.

Full text
Abstract:
The families of simplest cubic, simplest quartic and simplest sextic fields and the related Thue equations are well known, see G. Lettl, A. Pethő and P. Voutier, Simple families of Thue inequalities, Trans. Amer. Math. Soc. 351 (1999) 1871–1894, On the arithmetic of simplest sextic fields and related Thue equations, in Number Theory: Diophantine, Computational and Algebraic Aspects, eds. K. Győry et al. (de Gruyter, Berlin, 1998), pp. 331–348. The family of simplest cubic Thue equations was already studied in the relative case, over imaginary quadratic fields. In the present paper, we give a similar extension of simplest quartic and simplest sextic Thue equations over imaginary quadratic fields. We explicitly give the solutions of these infinite parametric families of Thue equations over arbitrary imaginary quadratic fields.
APA, Harvard, Vancouver, ISO, and other styles
2

Hurley, A. C., and A. K. Head. "Explicit Galois resolvents for sextic equations." International Journal of Quantum Chemistry 31, no. 3 (1987): 345–59. http://dx.doi.org/10.1002/qua.560310306.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Lee, Yang-Hi. "On the Hyers-Ulam-Rassias Stability of a General Quintic Functional Equation and a General Sextic Functional Equation." Mathematics 7, no. 6 (2019): 510. http://dx.doi.org/10.3390/math7060510.

Full text
Abstract:
The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers–Ulam–Rassias stability of the general quintic functional equation and the general sextic functional equation.
APA, Harvard, Vancouver, ISO, and other styles
4

Gaál, István, and László Remete. "Power integral bases in a family of sextic fields with quadratic subfields." Tatra Mountains Mathematical Publications 64, no. 1 (2015): 59–66. http://dx.doi.org/10.1515/tmmp-2015-0041.

Full text
Abstract:
Abstract Let M = Q(i √d) be any imaginary quadratic field with a positive square-free d. Consider the polynomial f(x) = x3 − ax2 − (a + 3)x − 1 with a parameter a ∈ ℤ. Let K = M(α), where α is a root of f. This is an infinite parametric family of sextic fields depending on two parameters, a and d. Applying relative Thue’s equations we determine the relative power integral bases of these sextic fields over their quadratic subfields. Using these results we also determine generators of (absolute) power integral bases of the sextic fields.
APA, Harvard, Vancouver, ISO, and other styles
5

Togbé, Alain. "A parametric family of sextic Thue equations." Acta Arithmetica 125, no. 4 (2006): 347–61. http://dx.doi.org/10.4064/aa125-4-4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Hagedorn, Thomas R. "General Formulas for Solving Solvable Sextic Equations." Journal of Algebra 233, no. 2 (2000): 704–57. http://dx.doi.org/10.1006/jabr.2000.8428.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Hu, Shuangnian, and Rongquan Feng. "On the number of solutions of two-variable diagonal sextic equations over finite fields." AIMS Mathematics 7, no. 6 (2022): 10554–63. http://dx.doi.org/10.3934/math.2022588.

Full text
Abstract:
<abstract><p>Let $ p $ be a prime, $ k $ a positive integer, $ q = p^k $, and $ \mathbb{F}_q $ be the finite field with $ q $ elements. In this paper, by using the Jacobi sums, we give an explicit formula for the number of solutions of the two-variable diagonal sextic equations $ x_1^6+x_2^6 = c $ over $ \mathbb{F}_q $, with $ c\in\mathbb{F}_q^* $ and $ p\equiv1({\rm{mod}} \ 6) $. Furthermore, by using the reduction formula for Jacobi sums, the number of solutions of the diagonal sextic equations $ x_1^6+x_2^6+\cdots+x_n^6 = c $ of $ n\geq3 $ variables with $ c\in\mathbb{F}_q^* $ and $ p\equiv1({\rm{mod}} \ 6) $, can also be deduced.</p></abstract>
APA, Harvard, Vancouver, ISO, and other styles
8

Bilu, Yuri, István Gaál, and Kálmán Győry. "Index form equations in sextic fields: a hard computation." Acta Arithmetica 115, no. 1 (2004): 85–96. http://dx.doi.org/10.4064/aa115-1-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Hoshi, Akinari. "On the simplest sextic fields and related Thue equations." Functiones et Approximatio Commentarii Mathematici 47, no. 1 (2012): 35–49. http://dx.doi.org/10.7169/facm/2012.47.1.3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Kulkarni, Raghavendra G. "Insert a Root to Extract a Root of Quintic Quickly." Annales Mathematicae Silesianae 33, no. 1 (2019): 153–58. http://dx.doi.org/10.2478/amsil-2018-0013.

Full text
Abstract:
AbstractThe usual way of solving a solvable quintic equation has been to establish more equations than unknowns, so that some relation among the coefficients comes up, leading to the solutions. In this paper, a relation among the coefficients of a principal quintic equation is established by effecting a change of variable and inserting a root to the quintic equation, and then equating odd-powers of the resulting sextic equation to zero. This leads to an even-powered sextic equation, or equivalently a cubic equation; thus one needs to solve the cubic equation.We break from this tradition, rather factor the even-powered sextic equation in a novel fashion, such that the inserted root is identified quickly along with one root of the quintic equation in a quadratic factor of the form, u2− g2 = (u + g)(u − g). Thus there is no need to solve any cubic equation. As an extra benefit, this root is a function of only one coefficient of the given quintic equation.
APA, Harvard, Vancouver, ISO, and other styles
More sources
You might also be interested in the extended bibliographies on the topic 'Sextic Equations' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography