Explicit t-expansions for the elliptic curve y2=4(x3 + Ax plus B)

被引：3

作者：

Yasuda, Seidai ^{[1
]}

机构：

[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5608502, Japan

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2013年 / 89卷 / 09期

关键词：

Elliptic curves; invariant differential; sigma function;

D O I：

10.3792/pjaa.89.123

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an elliptic curve E : y(2) = 4(x(3) + Ax + B) over a field of characteristic not equal 2, we explicitly compute the pullback to the formal completion of E at the origin of some important objects on E including the functions x, y and the invariant differential w = dx/y in terms of the formal parameter t = -2x/y.

引用

页码：123 / 127

页数：5

共 7 条

[1]

[Anonymous], 1979, COMPLEX ANAL

[2]

[Anonymous], 1986, GRADUATE TEXTS MATH

[3]

Aomoto K, 2011, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-4-431-53938-4_1

[4] ALGEBRAIC THETA FUNCTIONS AND THE p-ADIC INTERPOLATION OF EISENSTEIN-KRONECKER NUMBERS [J].

Bannai, Kenichi ;

Kobayashi, Shinichi .

DUKE MATHEMATICAL JOURNAL, 2010, 153 (02) :229-295

[5]

BEUKERS F., PREPRINT

[6]

Sadek M., ARXIV13036706

[7] ON THE PICARD-FUCHS EQUATION AND THE FORMAL BRAUER GROUP OF CERTAIN ELLIPTIC K3-SURFACES [J].

STIENSTRA, J ;

BEUKERS, F .

MATHEMATISCHE ANNALEN, 1985, 271 (02) :269-304

← 1 →