AN EFFECTIVE CRITERION FOR PERIODICITY OF l-ADIC CONTINUED FRACTIONS

被引：22

作者：

Capuano, Laura ^{[1
]}

Veneziano, Francesco ^{[2
]}

Zannier, Umberto ^{[3
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[2] Ctr Ric Matemat Ennio De Giorgi, Piazza Cavalieri 3, I-56126 Pisa, Italy

[3] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy

来源：

MATHEMATICS OF COMPUTATION | 2019年 / 88卷 / 318期

关键词：

D O I：

10.1090/mcom/3385

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The theory of continued fractions has been generalized to l-adic numbers by several authors and presents many differences with respect to the real case. In the present paper we investigate the expansion of rationals and quadratic irrationals for the l-adic continued fractions introduced by Ruban. In this case, rational numbers may have a periodic non-terminating continued fraction expansion; moreover, for quadratic irrational numbers, no analogue of Lagrange's theorem holds. We give general explicit criteria to establish the periodicity of the expansion in both the rational and the quadratic case (for rationals, the qualitative result is due to Laohakosol.

引用

页码：1851 / 1882

页数：32

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