Decomposition of primes in number fields defined by trinomials
Journal de théorie des nombres de Bordeaux, Volume 3 (1991) no. 1, p. 27-41

In this paper we deal with the problem of finding the prime-ideal decomposition of a prime integer in a number field K defined by an irreducible trinomial of the type X p m +AX+B[X], in terms of A and B. We also compute effectively the discriminant of K.

Keywords: decomposition of primes, discriminant, trinomials
@article{JTNB_1991__3_1_27_0,
     author = {Llorente, P. and Nart, Enric and Vila, N\'uria},
     title = {Decomposition of primes in number fields defined by trinomials},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {3},
     number = {1},
     year = {1991},
     pages = {27-41},
     zbl = {0733.11039},
     mrnumber = {1116099},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_1991__3_1_27_0}
}
Llorente, P.; Nart, E.; Vila, N. Decomposition of primes in number fields defined by trinomials. Journal de théorie des nombres de Bordeaux, Volume 3 (1991) no. 1, pp. 27-41. http://www.numdam.org/item/JTNB_1991__3_1_27_0/

[1] P. Llorente - E. Nart, Effective determination of the decomposition of the rational primes in a cubic field, Proc. Amer. Math. Soc. 87 (1983), 579-585. | MR 687621 | Zbl 0514.12003

[2] P. Llorente - E. Nart - N. Vila, Discriminants of number fields defined by trinomials, Acta Arith. 43 (1984), 367-373. | MR 756288 | Zbl 0493.12010

[3] Ö. Ore, Zur Theorie der algebraischen Körper, Acta Math. 44 (1923), 219-314. | JFM 49.0698.04

[4] Ö. Ore, Newtonsche Polygone in der Theorie des algebraischen Körper, math. Ann. 99 (1928), 84-117. | JFM 54.0191.02 | MR 1512440

[5] R.G. Swan, Factorization of polynomials over finite fields, Pacific J. Math. 12 (1962), 1099-1106. | MR 144891 | Zbl 0113.01701

[6] W.Y. Vélez, The factorization of p in Q(a1/pk ) and the genus field of Q(a1/n), Tokyo J. Math. 11 (1988), 1-19. | MR 947943 | Zbl 0664.12003