Using elliptic curves of rank one towards the undecidability of Hilbert's Tenth Problem over rings of algebraic integers

Details Using elliptic curves of rank one towards the undecidability of Hilbert's Tenth Problem over rings of algebraic integers Using elliptic curves of rank one towards the undecidability of Hilbert's Tenth Problem over rings of algebraic integers

2002-03-29

arxiv.org/abs/math/0204001v1

Mathematics

Number Theory

10 pages, Latex 2e. This article will appear in the Proceedings of the Algorithmic Number Theory Symposium V, in the Springer

Scientific paper

Let F and K be number fields, with F contained in K. and let O_F and O_K be
their rings of integers. If there exists an elliptic curve E over F such that
E(F) and E(K) have rank 1, then there exists a diophantine definition of O_F
over O_K.

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