ON THE FINITENESS OF p-ADIC CONTINUED FRACTIONS FOR NUMBER FIELDS

被引：6

作者：

Capuano, Laura ^{[1
]}

Murru, Nadir ^{[2
]}

Terracini, Lea ^{[3
]}

机构：

[1] Univ Roma Tre, Dipartimento Matemat Fis, Rome, Italy

[2] Univ Trento, Dipartimento Matemat, Trento, Italy

[3] Univ Torino, Dipartimento Informat, Turin, Italy

来源：

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE | 2022年 / 150卷 / 04期

关键词：

p-adic continued fractions; finiteness; Weil height; normEuclidean fields; norm-Euclidean class;

D O I：

10.24033/bsmf.2860

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a prime ideal p of the ring of integers of a number field K, we give a general definition of a p-adic continued fraction, which also includes classical definitions of continued fractions in the field of p-adic numbers. We give some necessary and sufficient conditions on K ensuring that for all but finitely many p, every alpha is an element of K admits a finite p-adic continued fraction expansion, addressing a similar problem posed by Rosen in the archimedean setting.

引用

页码：743 / 772

页数：30

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