Location of Small Points on an Elliptic Curve by an Equidistribution Argument
Copyright policy )Location of Small Points on an Elliptic Curve by an Equidistribution Argument
Abstract Let $E$ be an elliptic curve defined over a number field $K$ without complex multiplication. If $\Gamma \subset E(\overline{K})$ is a subgroup of finite rank, a very special case of a conjecture of Rémond predicts that points of small height in $E(K(\Gamma ))$ lie in the division group of $\Gamma $. Using an equidistribution argument, we will show that this conjecture is true for groups of rank arbitrarily large.
- Chinese Academy of Sciences China (People's Republic of)
- Academy of Mathematics and Systems Science China (People's Republic of)
Supersingular elliptic curve, Multiplication (music), Study of Finite Groups and Graphs, Complex multiplication, Limits and Structures in Graph Theory, Argument (complex analysis), Biochemistry, Algebraic Geometry and Moduli Theory, Elliptic curve, FOS: Mathematics, Discrete Mathematics and Combinatorics, Conjecture, Number Theory (math.NT), Mathematics - Number Theory, Representation Theory, Arithmetic, Pure mathematics, Finite field, Division (mathematics), Chemistry, Rank (graph theory), Combinatorics, Elliptic curves over global fields, Physical Sciences, Geometry and Topology, General theory of distribution modulo \(1\), Mathematics
Supersingular elliptic curve, Multiplication (music), Study of Finite Groups and Graphs, Complex multiplication, Limits and Structures in Graph Theory, Argument (complex analysis), Biochemistry, Algebraic Geometry and Moduli Theory, Elliptic curve, FOS: Mathematics, Discrete Mathematics and Combinatorics, Conjecture, Number Theory (math.NT), Mathematics - Number Theory, Representation Theory, Arithmetic, Pure mathematics, Finite field, Division (mathematics), Chemistry, Rank (graph theory), Combinatorics, Elliptic curves over global fields, Physical Sciences, Geometry and Topology, General theory of distribution modulo \(1\), Mathematics
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