On divisibility of $h^+$ by the prime $5$

Stanislav Jakubec

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Displaying similar documents to “On divisibility of $h^{+}$ by the prime $5$ ”

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

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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.

Equicontinuity and Convergent Sequences in the Spaces $_{C}^{'}$ and $_{M}$

Jan Kisyński (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Characterizations of equicontinuity and convergent sequences are given for the space $_{C}^{'} (ℝ ⁿ)$ of rapidly decreasing distributions and the space $_{M} (ℝ ⁿ)$ of slowly increasing infinitely differentiable functions.

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The existence of $P (α)$ -points of N* for $ℵ_{0} α < 𝔠$

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On the $2$ -class group of some number fields with large degree

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini (2021)

Archivum Mathematicum

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Let $d$ be an odd square-free integer, $m \geq 3$ any integer and $L_{m, d} : = ℚ (ζ_{2^{m}}, \sqrt{d})$ . In this paper, we shall determine all the fields $L_{m, d}$ having an odd class number. Furthermore, using the cyclotomic $ℤ_{2}$ -extensions of some number fields, we compute the rank of the $2$ -class group of $L_{m, d}$ whenever the prime divisors of $d$ are congruent to $3$ or $5 (mod 8)$ .