Decomposition of primes in number fields defined by trinomials

P. Llorente; E. Nart; N. Vila

doi:10.5802/jtnb.40

P. Llorente; E. Nart; N. Vila

Journal de Théorie des Nombres de Bordeaux, Volume 3 (1991) no. 1, pp. 27-41.

Abstract

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 $X^{p^{m}} + A X + B \in ℤ [X]$ , in terms of $A$ and $B$ . We also compute effectively the discriminant of $K$ .

MR: 1116099 | Zbl: 0733.11039

DOI: 10.5802/jtnb.40
Keywords: decomposition of primes, discriminant, trinomials

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P. Llorente; E. Nart; N. Vila. Decomposition of primes in number fields defined by trinomials. Journal de Théorie des Nombres de Bordeaux, Volume 3 (1991) no. 1, pp. 27-41. doi : 10.5802/jtnb.40. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.40/

References
Cited by

[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

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