From Pólya fields to Pólya groups (II) Non-Galois number fields

  title={From P{\'o}lya fields to P{\'o}lya groups (II) Non-Galois number fields},
  author={Jean-Luc Chabert},
  journal={arXiv: Number Theory},

P\'olya-Ostrowski Group and Unit Index in Real Biquadratic Fields

Pólya group of a Galois number field K is the subgroup of the ideal class group of K generated by all strongly ambiguous ideal classes. In this paper, using Galois cohomology and some results in [14,

Pre-Pólya group in even dihedral extensions of ℚ

Investigating on Pólya groups [P. J. Cahen and J. L. Chabert Integer-Valued Polynomials, Mathematical Surveys and Monographs, Vol. 48 (American Mathematical Society, Providence, 1997)] in non-Galois

Ostrowski quotients for finite extensions of number fields

. For L/K a finite Galois extension of number fields, the relative P´olya group Po( L/K ) coincides with the group of strongly ambiguous ideal classes in L/K . In this paper, using a well known exact



Global restrictions on ramification in number fields

Let G be the Galois group of a number field extension. For each primep a map ε(p)∶H2(G,{±1})→{±1} is defined. This local symbol has a global restriction: the product of ε(p) over all primes is


Let G be a subgroup of the symmetric group S n , and let δ G =∣ S n / G ∣ −1 where ∣ S n / G ∣ is the index of G in S n . Then there are at most O n ,ϵ ( H n −1+ δ G +ϵ ) monic integer polynomials of

Integer valued polynomials over a number field

A number field is called a Pólya field if the module of integer valued polynomials over that field is generated by (fi)i=0∞ over the ring of integers, with deg(fi)=i, i=0, 1, 2,... In this paper

A computation concerning doubly transitive permutation groups.

Let G be a transitive permutation group on a fmite set Ω. Fix an element α of Ω. We introduce the following notation: Ga is the stabilizer of α in G; G'x is the commutator subgroup of Ga ; T is the

Generalized Factorials and Fixed Divisors over Subsets of a Dedekind Domain

Abstract Given a subsetXof a Dedekind domainD, and a polynomialF∈D[x], thefixed divisor d(X, F) ofFoverXis defined to be the ideal inDgenerated by the elementsF(a),a∈X. In this paper we derive a

Algebraic Number Theory

I: Algebraic Integers.- II: The Theory of Valuations.- III: Riemann-Roch Theory.- IV: Abstract Class Field Theory.- V: Local Class Field Theory.- VI: Global Class Field Theory.- VII: Zeta Functions


Let R be a Krull ring with quotient field K and a1, . . . , an in R. If and only if the ai are pairwise incongruent mod every height 1 prime ideal of infinite index in R does there exist for all

Über ganzwertige Polynome in algebraischen Zahlkörpern.

(1.) P(%) = «0^ + «i a?"" H + <*m ganzzahlig im Körper K, wenn die Koeffizienten «0, 1?... am ganze Zahlen von jST sind. Man nenne ein Polynom P ( x ) ganzwertig im Körper K, wenn für jede ganze Zahl