Counting discriminants of number fields

DOI10.5802/jtnb.559zbMath1193.11109OpenAlexW2153773719MaRDI QIDQ2642774

Michel Olivier, Henri Cohen, Francisco Diaz y Diaz

Publication date: 4 September 2007

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2006__18_3_573_0

zbMATH Keywords

Galois groupGalois closurediscriminants of number fields

Mathematics Subject Classification ID

Galois theory (11R32) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Class numbers, class groups, discriminants (11R29) Density theorems (11R45)

Related Items (18)

Counting cyclic quartic extensions of a number field ⋮ Constructing complete tables of quartic fields using Kummer theory ⋮ ON THE DISTRIBUTION OF CYCLIC NUMBER FIELDS OF PRIME DEGREE ⋮ Identities for field extensions generalizing the Ohno–Nakagawa relations ⋮ Enumerating quartic dihedral extensions of \(\mathbb Q\) with signatures. ⋮ The average least quadratic nonresidue modulo \(m\) and other variations on a theme of Erdős ⋮ The first negative Fourier coefficient of an Eisenstein series newform ⋮ Enumerating number fields ⋮ Counting 3-dimensional algebraic tori over \(\mathbb{Q}\) ⋮ On the probabilities of local behaviors in abelian field extensions ⋮ Splitting behavior of \(S_n\)-polynomials ⋮ Exact computation of the discriminants of Abelian extensions ⋮ Error estimates for the Davenport-Heilbronn theorems ⋮ Dirichlet series associated to cubic fields with given quadratic resolvent ⋮ Dirichlet series associated to quartic fields with given cubic resolvent ⋮ On the Colmez conjecture for non-abelian CM fields ⋮ Exact counting of $D_\ell $ number fields with given quadratic resolvent ⋮ Index, the prime ideal factorization in simplest quartic fields and counting their discriminants

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