# Hilbert's tenth problem

## Papers overview

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2010

2010

- 2010

In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fieldsâ€¦Â (More)

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2010

2010

- 2010

Let A(D) be any quadratic ring; in this paper we prove that Hilbert's tenth problem for A(D) is unsolvable, and we determineâ€¦Â (More)

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2008

2008

- IJAC
- 2008

We show a reduction of Hilbertâ€™s tenth problem to the solvability of the matrix equation A1 1 A i2 2 Â· Â· Â·A ik k = Z over nonâ€¦Â (More)

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Review

2008

Review

2008

- 2008

Following ideas of Poonen, we use elliptic divisibility sequences to construct two subrings of the field of rational numbersâ€¦Â (More)

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2007

2007

- 2007

Following ideas of Poonen, we use elliptic divisibility sequences to construct two subrings of the field of rational numbersâ€¦Â (More)

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Review

2005

Review

2005

- CiE
- 2005

This is a survey of a century long history of interplay between Hilbertâ€™s tenth problem (about solvability of Diophantineâ€¦Â (More)

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2004

2004

- 2004

Let K be the function field of a variety of dimension â‰¥ 2 over an algebraically closed field of characteristic zero. Then Hilbertâ€¦Â (More)

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2003

2003

- Arch. Math. Log.
- 2003

ABSTRACT Hilbert's Tenth problem on erned the de idability of Diophantine equations over the integers. Its negative solution, theâ€¦Â (More)

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2003

2003

- ArXiv
- 2003

We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbertâ€™sâ€¦Â (More)

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1992

1992

- Journal of Automated Reasoning
- 1992

We show that the problem of finding integer solutions to a polynomial equation over the integers has unification type zero, i.eâ€¦Â (More)

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