Skip to main content
Conference Proceedings

Using elliptic curves of rank one towards the undecidability of hilbert’s tenth problem over rings of algebraic integers

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2002) 2369 33-42
DOI: 10.1007/3-540-45455-1_4
34Citations
Citations of this article
1Readers
Mendeley users who have this article in their library.
Get full text

Abstract

Let F ⊆ K be number fields, and let OF and OK be their rings of integers. If there exists an elliptic curve E over F such that rk,E(F) = rk,E(K) = 1, then there exists a diophantine definition of OF over OK.

Cite

CITATION STYLE

APA

Poonen, B. (2002). Using elliptic curves of rank one towards the undecidability of hilbert’s tenth problem over rings of algebraic integers. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2369, pp. 33–42). Springer Verlag. https://doi.org/10.1007/3-540-45455-1_4

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free