On the Periodicity Problem for the Continued Fraction Expansion of Elements of Hyperelliptic Fields with Fundamental S-Units of Degree at Most 11

被引：2

作者：

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

Petrunin, M. M. ^{[1
]}

Shteinikov, Yu N. ^{[1
]}

机构：

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

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

来源：

DOKLADY MATHEMATICS | 2021年 / 104卷 / 02期

关键词：

hyperelliptic field; S-units; continued fractions; periodicity; torsion points; CUBIC POLYNOMIALS; ROOT-F; FINITENESS; NUMBER;

D O I：

10.1134/S1064562421050082

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We solve the problem of describing square-free polynomials f (x) is an element of k[x] with a periodic expansion of root f(x) into a functional continued fraction in k((x)), where k is a number field and the degree of the corresponding fundamental S-unit of the hyperelliptic field k(x)(root f(x)) is less than or equal to 11.

引用

页码：258 / 263

页数：6

共 14 条

[1]

Abel N.-H., 1826, J REINE ANGEW MATH, V1, P185

[2]

KUBERT DS, 1976, P LOND MATH SOC, V33, P193

[3] S-Units and Periodicity of Square Root in Hyperelliptic Fields [J].

Petrunin, M. M. .

DOKLADY MATHEMATICS, 2017, 95 (03) :222-225

[4]

Platonov VP, 2020, DOKL MATH, V102, P487, DOI 10.1134/S1064562420060137

[5]

Platonov VP, 2020, RUSS MATH SURV+, V75, P785, DOI [10.4213/rm9962, 10.1070/RM9962]

[6]

Platonov VP, 2020, DOKL MATH, V102, P288, DOI 10.1134/S1064562420040249

[7]

Platonov VP, 2019, DOKL MATH, V100, P440, DOI 10.1134/S1064562419050119

[8] On the Finiteness of Hyperelliptic Fields with Special Properties and Periodic Expansion of f [J].

Platonov, V. P. ;

Zhgoon, V. S. ;

Petrunin, M. M. ;

Shteinikov, Yu. N. .

DOKLADY MATHEMATICS, 2018, 98 (03) :641-645

[9] Groups of S-Units and the Problem of Periodicity of Continued Fractions in Hyperelliptic Fields [J].

Platonov, V. P. ;

Petrunin, M. M. .

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2018, 302 (01) :336-357

[10] On the problem of periodicity of continued fractions in hyperelliptic fields [J].

Platonov, V. P. ;

Fedorov, G., V .

SBORNIK MATHEMATICS, 2018, 209 (04) :519-559

← 1 2 →