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Note on the density constant in the distribution of self-numbers. II

G. Troi, U. Zannier (1999)

Bollettino dell'Unione Matematica Italiana

Dimostriamo che la costante che regola la distribuzione dei cosiddetti self numbers è un numero trascendente. Ciò precisa un risultato dimostrato in un precedente articolo dal medesimo titolo, ossia che tale costante sia irrazionale. Il metodo fa uso di una curiosa formula per l'espansione 2-adica di tale numero (già utilizzata nell'altro lavoro) e del profondo Teorema del Sottospazio.

Note on the diophantine equation 1 + x + x2 + ... + xn = ym.

A. Rotkiewicz (1987)

Elemente der Mathematik

Note on the Erdős-Graham theorem

Y.-F. S. Pétermann (2010)

Acta Arithmetica

Note on the fractional parts of λθⁿ

Masayoshi Hata (2005)

Acta Arithmetica

Note on the Galois module structure of quadratic extensions

Günter Lettl (1994)

Colloquium Mathematicae

In this note we will determine the associated order of relative extensions of algebraic number fields, which are cyclic of prime order p, assuming that the ground field is linearly disjoint to the pth cyclotomic field, $ℚ^{(p)}$ . For quadratic extensions we will furthermore characterize when the ring of integers of the extension field is free over the associated order. All our proofs are quite elementary. As an application, we will determine the Galois module structure of $ℚ^{(n)} / ℚ^{{(n)}^{+}}$ .

Note on the Hilbert 2-class field tower

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2022)

Mathematica Bohemica

Let $k$ be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields $𝕜 = ℚ (\sqrt{d}, \sqrt{- 1})$ , which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).