2022/04/09 by Daniel C. Mayer, Mayer, Daniel C., Abderazak Soullami +1
Mathematics · #11R04 #11R16 #11R20 #11R21 #11R27 #11R29 #11R37 #11Y40 #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2204.04474
openalex publication_date 2022/04/09 · openalex created_date 2022/04/15 · openalex updated_date 2026/08/01
For an infinite family of monogenic trinomials P(X) = X3± 3rbX-b in ℤ\lbrack X\rbrack, arithmetical invariants of the cubic number field L = ℚ(θ), generated by a zero θ of P(X), and of its Galois closure N = L(√(d(L))) are determined. The conductor f of the cyclic cubic relative extension N/K, where K = ℚ(√(d(L))) denotes the unique quadratic subfield of N, is proved to be of the form 3eb with e∈\lbrace 1,2\rbrace, which admits statements concerning primitive ambiguous principal ideals, lattice minima, and independent units in L. The number m of non-isomorphic cubic fields L1,…,Lm sharing a common discriminant d(Li) = d(L) with L is determined.