Counting rational points on smooth cubic curves
| Autor: | Manh Hung Tran |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Mathematics - Number Theory Rank (linear algebra) Diophantine equation 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Mathematics - Algebraic Geometry symbols.namesake Elliptic curve 11D25 11D45 11G05 Jacobian matrix and determinant FOS: Mathematics symbols Determinant method Counting points on elliptic curves Number Theory (math.NT) 0101 mathematics Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Journal of Number Theory. 189:138-146 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2017.12.001 |
| Popis: | We use a global version of Heath-Brown's $p-$adic determinant method developed by Salberger to give upper bounds for the number of rational points of height at most $B$ on non-singular cubic curves defined over $\mathbb{Q}$. The bounds are uniform in the sense that they only depend on the rank of the corresponding Jacobian. Comment: 10 pages. Comments are welcome |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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