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Totally real bi-quadratic fields with large Pólya groups.
- Source :
-
Research in Number Theory . 4/24/2022, Vol. 8 Issue 2, p1-6. 6p. - Publication Year :
- 2022
-
Abstract
- For an algebraic number field K with ring of integers O K , an important subgroup of the ideal class group C l K is the Pólya group, denoted by Po(K), which measures the failure of the O K -module I n t (O K) of integer-valued polynomials on O K from admitting a regular basis. In this paper, we prove that for any integer n ≥ 2 , there are infinitely many totally real bi-quadratic fields K with P o (K) ≃ (Z / 2 Z) n . In fact, we explicitly construct such an infinite family of number fields. This also provides an infinite family of bi-quadratic fields with ideal class groups of 2-ranks at least n. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 25220160
- Volume :
- 8
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Research in Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 156494400
- Full Text :
- https://doi.org/10.1007/s40993-022-00327-8