scholarly journals Formal groups, elliptic curves, and some theorems of Couveignes

1998 ◽  
pp. 482-501 ◽  
Author(s):  
Antonia W. Bluher
Keyword(s):  
Elliptic Curves ◽  
Formal Groups

scholarly journals FORMAL GROUPS AND INVARIANT DIFFERENTIALS OF ELLIPTIC CURVES

2015 ◽  
Vol 92 (1) ◽  
pp. 44-51
Author(s):  
MOHAMMAD SADEK
Keyword(s):  
Power Series ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Series Expansion ◽  
Power Series Expansion ◽  
Formal Groups ◽  
Frobenius Endomorphism ◽  
Congruence Relations ◽  
Invariant Differential ◽  
Weierstrass Equations

In this paper, we find a power series expansion of the invariant differential ${\it\omega}_{E}$ of an elliptic curve $E$ defined over $\mathbb{Q}$, where $E$ is described by certain families of Weierstrass equations. In addition, we derive several congruence relations satisfied by the trace of the Frobenius endomorphism of $E$.

FORMAL GROUPS OF JACOBIAN VARIETIES OF HYPERELLIPTIC CURVES

2010 ◽  
Vol 06 (07) ◽  
pp. 1701-1716
Author(s):  
FUMIO SAIRAIJI
Keyword(s):  
Elliptic Curves ◽  
Characteristic Zero ◽  
Hyperelliptic Curve ◽  
Hyperelliptic Curves ◽  
Formal Groups ◽  
Jacobian Varieties ◽  
Explicit Constructions ◽  
Modulo P

Let k be a field of characteristic zero. In this paper, we discuss two explicit constructions of the formal groups Ĵ of the Jacobian varieties J of hyperelliptic curves C over k. Our results are generalizations of the classical constructions of formal groups of elliptic curves. As an application of our results, we may decide the type of bad reduction of J modulo p when C is a hyperelliptic curve over ℚ.

Elliptic Curves

1997 ◽  
Author(s):  
Henry McKean ◽  
Victor Moll
Keyword(s):  
Elliptic Curves

The Joint Universality for L-Functions of Elliptic Curves

2004 ◽  
Vol 9 (4) ◽  
pp. 331-348
Author(s):  
V. Garbaliauskienė
Keyword(s):  
Elliptic Curves ◽  
Rational Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

A joint universality theorem in the Voronin sense for L-functions of elliptic curves over the field of rational numbers is proved.

Sign in / Sign up

Export Citation Format

Share Document