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Article Dans Une Revue Filomat Année : 2020

Index, the prime ideal factorization in simplest quartic fields and counting their discriminants

Résumé

We consider the simplest quartic number fields Km defined by the irreducible quartic polynomials x4-mx3-6x2+mx+1, where m runs over the positive rational integers such that the odd part of m2+16 is square free. In this paper, we study the index I(Km) and determine the explicit prime ideal factorization of rational primes in simplest quartic number fields Km. On the other hand, we establish an asymptotic formula for the number of simplest quartic fields with discriminant ? x and given index.
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Dates et versions

hal-04458821 , version 1 (04-04-2024)

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Abdelmejid Bayad, Mohammed Seddik. Index, the prime ideal factorization in simplest quartic fields and counting their discriminants. Filomat, 2020, 34 (2), pp.591-600. ⟨10.2298/FIL2002591B⟩. ⟨hal-04458821⟩
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