Bjorn Poonen  Home/Search
Context Related
| berkeley.edu/~poonen/papers...ants5.pdf Cached: PDF This document uses CoBlitz to cache paper downloads. If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
PS.gz PS Image Update HelpFrom: berkeley.edu/~poonen/ (more) (Enter author homepages) |
Rate this article:      (best)Comment on this article |
Abstract: Let F 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 . (Update)
Cited by: More
Hilbert's Tenth Problem over Rings of Number-Theoretic Interest - Poonen (2003) (Correct)
Active bibliography (related documents): More All
1.6: Diophantine Undecidability of Function Fields of Characteristic .. - Shlapentokh (2001) (Correct)
1.6: Defining Integrality at Prime Sets of High Density over.. - Shlapentokh (2001) (Correct)
1.2: On Diophantine definability and decidability in some infinite.. - Shlapentokh (2001) (Correct)
Similar documents based on text: More All
0.2: Hilbert's Tenth Problem and Mazur's Conjecture for Large Subrings .. - Poonen (2003) (Correct)
0.2: Computing Rational Points on Curves - Poonen (2000) (Correct)
0.2: A Structural Approach to Diophantine Definability - Prunescu (1999) (Correct)
BibTeX entry: (Update)
Bjorn Poonen, Using elliptic curves of rank one towards the undecidability of hilbert's tenth problem over rings of algebraic integers, Algorithmic Number Theory, C. Fieker and D. Kohel (eds.), 5th International Symposium, ANTS-V, Sydney, Australia, July http://citeseer.ist.psu.edu/602328.html More
@misc{ poonen-using,
author = "B. Poonen",
title = "Using elliptic curves of rank one towards the undecidability of hilbert's
tenth problem over rings of algebraic integers",
text = "Bjorn Poonen, Using elliptic curves of rank one towards the undecidability
of hilbert's tenth problem over rings of algebraic integers, Algorithmic
Number Theory, C. Fieker and D. Kohel (eds.), 5th International Symposium,
ANTS-V, Sydney, Australia, July",
url = "citeseer.ist.psu.edu/602328.html" }
Citations (may not include all citations):237 The arithmetic of elliptic curves (context) - Silverman
15 The decision problem for exponential diophantine equations (context) - Davis, Putnam et al. - 1961
6 Hilbert's tenth problem for a class of rings of algebraic in.. (context) - Pheidas - 1988
6 Translated from the French and edited by Martin Brown from n.. (context) - Serre, the et al. - 1997
6 Diophantine sets over some rings of algebraic integers (context) - Denef, Lipshitz - 1978
5 Questions of decidability and undecidability in number theor.. (context) - Mazur - 1994 ACM DBLP
5 Extension of Hilbert's tenth problem to some algebraic numbe.. (context) - Shlapentokh - 1989
5 Hilbert's tenth problem for fields of rational functions ove.. (context) - Pheidas - 1991
4 Hilbert's tenth problem: relations with arithmetic and algeb.. (context) - Denef, Lipshitz et al.
4 Diophantine undecidability of C (context) - Kim, Roush - 1992
4 Hilbert's tenth problem for algebraic function fields over i.. (context) - Shlapentokh - 2000
4 Hilbert's tenth problem for rational function fields in char.. (context) - Videla - 1994
3 Arithmetical problems and recursively enumerable predicates (context) - Davis - 1953 DBLP
2 Hilbert's tenth problem for rings of algebraic functions in .. (context) - Shlapentokh - 1992
2 Hilbert's tenth problem over number fields (context) - Shlapentokh
2 The Diophantineness of enumerable sets (context) - Matijasevic - 1970
2 Diophantine sets over algebraic integer rings (context) - Denef - 1980
1 extending results presented in a lecture 18 June 2001 at a c.. (context) - Moret-Bailly, preparation - 2001
1 University of California (context) - Eisentrager, thesis
Documents on the same site (http://math.berkeley.edu/~poonen/): More
Zeros Of Sparse Polynomials Over Local Fields Of Characteristic p - Poonen (Correct)
Bertini Theorems over Finite Fields - Poonen (2002) (Correct)
Squarefree Values of Multivariable Polynomials - Poonen (2001) (Correct)
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC