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Subjects
11-XX Number theory
11Rxx Algebraic number theory: global fields
11R16 Cubic and quartic extensions

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Displaying 1 – 9 of 9

Racines cubiques de nombres entiers et multiplication complexe dans les fonctions elliptiques

D. Mirimanoff (1903)

Mathematische Annalen

Ramification in quartic cyclic number fields $K$ generated by $x^{4} + p x^{2} + p$

Julio Pérez-Hernández, Mario Pineda-Ruelas (2021)

Mathematica Bohemica

If $K$ is the splitting field of the polynomial $f (x) = x^{4} + p x^{2} + p$ and $p$ is a rational prime of the form $4 + n^{2}$ , we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q 𝒪_{K}$ , where $q$ is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.

Ranks of 3-class groups of non-Galois cubic fields

Frank Gerth (1976)

Acta Arithmetica

Rational quartic reciprocity

Franz Lemmermeyer (1994)

Acta Arithmetica

Rational quartic reciprocity II

Franz Lemmermeyer (1997)

Acta Arithmetica

Real zeros of the Dedekind zeta function of an imaginary quadratic field

M.E. Low (1968)

Acta Arithmetica

Recherches analytiques sur la surface du troisième ordre qui est la réciproque de la surface de Steiner

Laguerre (1873)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Relative integral basis for algebraic number fields.

Haghighi, Mahmood (1986)

International Journal of Mathematics and Mathematical Sciences

Representation of primes by the principal form of discriminant -D when the classnumber h(-D) is 3

Kenneth Williams, Richard Hudson (1991)

Acta Arithmetica

Currently displaying 1 – 9 of 9

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