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  • Tome 2 (2010)
  • no. 2
  • p. 21-26
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no. 2

Pólya fields and Pólya numbers
Amandine Leriche
Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 21-26.
  • Résumé

A number field K, with ring of integers 𝒪 K , is said to be a Pólya field if the 𝒪 K -algebra formed by the integer-valued polynomials on 𝒪 K admits a regular basis. In a first part, we focus on fields with degree less than six which are Pólya fields. It is known that a field K is a Pólya field if certain characteristic ideals are principal. Analogously to the classical embedding problem, we consider the embedding of K in a Pólya field. We give a positive answer to this embedding problem by showing that the Hilbert class field H K of K is a Pólya field. Finally, we give upper bounds for the minimal degree po K of a Pólya field containing K, namely the Pólya number of K.

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Publié le : 2011-10-20
DOI : https://doi.org/10.5802/acirm.29
Classification : 11R04,  13F20,  11R16,  11R37
Mots clés : Pólya fields, Hilbert class field, genus field, integer-valued polynomials
@article{ACIRM_2010__2_2_21_0,
     author = {Amandine Leriche},
     title = {P\'olya fields and P\'olya numbers},
     journal = {Actes des rencontres du CIRM},
     pages = {21--26},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     doi = {10.5802/acirm.29},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.29/}
}
Leriche, Amandine. Pólya fields and Pólya numbers. Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 21-26. doi : 10.5802/acirm.29. https://acirm.centre-mersenne.org/articles/10.5802/acirm.29/
  • Bibliographie

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[9] A. Leriche, Groupes, Corps et Extensions de Pólya : une question de capitulation, PhD thesis, Université de Picardie Jules Verne (Décembre 2010).

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[11] A. Ostrowski, Über ganzwertige Polynome in algebraischen Zahlkörpren, J. Reine Angew. Math. 149 (1919), 117-124.

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