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https://doi.org/10.3336/gm.53.2.04

Trinomials ax8+bx+c with Galois groups of order 1344

Szabolcs Tengely ; Institute of Mathematics, University of Debrecen, P.O.Box 12, 4010 Debrecen , Hungary

Puni tekst: engleski, pdf (141 KB) str. 265-273 preuzimanja: 212* citiraj
APA 6th Edition
Tengely, S. (2018). Trinomials ax8+bx+c with Galois groups of order 1344. Glasnik matematički, 53 (2), 265-273. https://doi.org/10.3336/gm.53.2.04
MLA 8th Edition
Tengely, Szabolcs. "Trinomials ax8+bx+c with Galois groups of order 1344." Glasnik matematički, vol. 53, br. 2, 2018, str. 265-273. https://doi.org/10.3336/gm.53.2.04. Citirano 28.10.2021.
Chicago 17th Edition
Tengely, Szabolcs. "Trinomials ax8+bx+c with Galois groups of order 1344." Glasnik matematički 53, br. 2 (2018): 265-273. https://doi.org/10.3336/gm.53.2.04
Harvard
Tengely, S. (2018). 'Trinomials ax8+bx+c with Galois groups of order 1344', Glasnik matematički, 53(2), str. 265-273. https://doi.org/10.3336/gm.53.2.04
Vancouver
Tengely S. Trinomials ax8+bx+c with Galois groups of order 1344. Glasnik matematički [Internet]. 2018 [pristupljeno 28.10.2021.];53(2):265-273. https://doi.org/10.3336/gm.53.2.04
IEEE
S. Tengely, "Trinomials ax8+bx+c with Galois groups of order 1344", Glasnik matematički, vol.53, br. 2, str. 265-273, 2018. [Online]. https://doi.org/10.3336/gm.53.2.04

Sažetak
Bruin and Elkies ([7]) obtained the curve of genus 2 parametrizing trinomials ax8 + bx + c whose Galois group is contained in G1344 = (ℤ/2)3 ⋊ G168. They found some rational points of small height and computed the associated trinomials. They conjecture that the only ℚ-rational points of the hyperelliptic curve

Y2 = 2X6 + 28X5 + 196X4 + 784X3 + 1715X2 + 2058X + 2401

are given by (X, Y ) = (0, ± 49), (-1, ± 38), (-3, ± 32), and (-7, ± 196). In this paper we prove that the above points are the only S-integral points with S={2,3,5,7,11,13,17,19}.

Ključne riječi
Trinomials; hyperelliptic curves; S-integral points

Hrčak ID: 214475

URI
https://hrcak.srce.hr/214475

Posjeta: 348 *