Add to ORKGWe exhibit a genus{2 curve C de ned over Q(T ) which admits two independent morphisms to a rank{1 elliptic curve de ned over Q(T ). We describe completely the set of Q(T ){rational points of the curve C and obtain a uniform bound for the number of Q{rational points of a rational specialization C t of the curve C for a certain (possibly in nite) set of values t 2 Q. Furthermore, for this set of values t 2 Q we describe completely the set of Q{rational points of the curve C t . Finally we show how these results can be strengthened assuming a height conjecture of S. Lang
Abstract. Let Nq(g) denote the maximal number of Fq-rational points on any curve of genus g over Fq....
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.Cataloged fro...
We give asymptotics for the number of isomorphism classes of elliptic curves over arbitrary number f...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
The paper proves uniform bounds for the number of rational points of bounded height on certain ellip...
The paper proves uniform bounds for the number of rational points of bounded height on certain ellip...
Let E m be the family of elliptic curves given by y^2=x^3-x+m^2, which has rank 2 when regarded as a...
Minor revisionsFor a given genus $g \geq 1$, we give lower bounds for the maximal number of rational...
In elliptic curve theory, number of rational points on elliptic curves and determination of these po...
We discuss a technique for trying to find all rational points on curves of the form $Y^2 = f_3 X^6 +...
We introduce a general strategy for proving quantitative and uniform bounds on the number of common ...
We discuss a technique for trying to find all rational points on curves of the form $Y^2 = f_3 X^6 +...
This thesis contains two papers dealing with counting problems for curves of genusone. We obtain uni...
We construct families of curves which provide counterexamples for a uniform boundedness question. ...
Abstract. Let Nq(g) denote the maximal number of Fq-rational points on any curve of genus g over Fq....
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.Cataloged fro...
We give asymptotics for the number of isomorphism classes of elliptic curves over arbitrary number f...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
The paper proves uniform bounds for the number of rational points of bounded height on certain ellip...
The paper proves uniform bounds for the number of rational points of bounded height on certain ellip...
Let E m be the family of elliptic curves given by y^2=x^3-x+m^2, which has rank 2 when regarded as a...
Minor revisionsFor a given genus $g \geq 1$, we give lower bounds for the maximal number of rational...
In elliptic curve theory, number of rational points on elliptic curves and determination of these po...
We discuss a technique for trying to find all rational points on curves of the form $Y^2 = f_3 X^6 +...
We introduce a general strategy for proving quantitative and uniform bounds on the number of common ...
We discuss a technique for trying to find all rational points on curves of the form $Y^2 = f_3 X^6 +...
This thesis contains two papers dealing with counting problems for curves of genusone. We obtain uni...
We construct families of curves which provide counterexamples for a uniform boundedness question. ...
Abstract. Let Nq(g) denote the maximal number of Fq-rational points on any curve of genus g over Fq....
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.Cataloged fro...
We give asymptotics for the number of isomorphism classes of elliptic curves over arbitrary number f...