All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 11 of 11

Showing per page

Solutions of cubic equations in quadratic fields

K. Chakraborty, Manisha V. Kulkarni (1999)

Acta Arithmetica

Let K be any quadratic field with K its ring of integers. We study the solutions of cubic equations, which represent elliptic curves defined over ℚ, in quadratic fields and prove some interesting results regarding the solutions by using elementary tools. As an application we consider the Diophantine equation r+s+t = rst = 1 in K . This Diophantine equation gives an elliptic curve defined over ℚ with finite Mordell-Weil group. Using our study of the solutions of cubic equations in quadratic fields...

Some applications of decomposable form equations to resultant equations

K. Győry (1993)

Colloquium Mathematicae

1. Introduction. The purpose of this paper is to establish some general finiteness results (cf. Theorems 1 and 2) for resultant equations over an arbitrary finitely generated integral domain R over ℤ. Our Theorems 1 and 2 improve and generalize some results of Wirsing [25], Fujiwara [6], Schmidt [21] and Schlickewei [17] concerning resultant equations over ℤ. Theorems 1 and 2 are consequences of a finiteness result (cf. Theorem 3) on decomposable form equations over R. Some applications of Theorems...

Currently displaying 1 – 11 of 11

Page 1