Relative Pólya group and Pólya dihedral extensions of \(\mathbb{Q}\)

DOI10.1016/j.jnt.2019.07.016zbMath1457.11143arXiv1807.04744OpenAlexW2971278765MaRDI QIDQ2329280

Ali Rajaei, Abbas Maarefparvar

Publication date: 17 October 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.04744

zbMATH Keywords

integer valued polynomialsPólya fieldsdihedral extensionsPólya grouprelative Pólya group

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Class field theory (11R37) Class numbers, class groups, discriminants (11R29) Ramification and extension theory (11S15) Algebraic numbers; rings of algebraic integers (11R04) Galois cohomology (11R34)

Related Items (7)

Totally real bi-quadratic fields with large Pólya groups ⋮ On quadratic Ostrowski extensions of imaginary quadratic fields ⋮ Ostrowski quotients for finite extensions of number fields ⋮ Pre-Pólya group in even dihedral extensions of ℚ ⋮ Pólya group in some real biquadratic fields ⋮ Existence of relative integral basis over quadratic fields and Pólya property ⋮ From Pólya fields to Pólya groups. I: Galois extensions

Cites Work

• Pólya fields, Pólya groups and Pólya extensions: a question of capitulation
• Biquadratic Pólya fields with only one quadratic Pólya subfield
• About the embedding of a number field in a Pólya field
• Some non-Pólya biquadratic fields with low ramification
• Cubic, quartic and sextic Pólya fields
• Integer valued polynomials over a number field
• A note on class number of algebraic number fields
• Integer-Valued Polynomials
• Advanced Topics in Computional Number Theory
• Class Number and Ramification in Number Fields
• Class field theory
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