S-units and periodicity of continued fractions in hyperelliptic fields

被引：9

作者：

Platonov, V. P. ^{[1
,2
]}

Fedorov, G. V. ^{[1
,3
]}

机构：

[1] Russian Acad Sci, Res Inst Syst Dev, Moscow 117218, Russia

[2] Russian Acad Sci, Steklov Inst Math, Moscow 119991, Russia

[3] Moscow MV Lomonosov State Univ, Mech & Math Fac, Moscow 119991, Russia

来源：

DOKLADY MATHEMATICS | 2015年 / 92卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Steklov Institute; Continue Fraction; DOKLADY Mathematic; Formal Power Series; Period Length;

D O I：

10.1134/S1064562415060319

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let L be the function field of a hyperelliptic curve defined over any field of characteristic different from 2, and let S be a set consisting of an infinite and a finite valuation of L. A relationship between the problem of the existence of nontrivial S-units in the field L and the periodicity of the continued fraction expansion of certain key elements of L is discovered for the first time for finite valuations.

引用

页码：752 / 756

页数：5

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