Hilbert's tenth problem

Known as: Hilbert's 10th problem, Hilberts tenth problem, 10th Hilbert problem 
Hilbert's tenth problem is the tenth on the list of Hilbert's problems of 1900. Its statement is as follows: Given a Diophantine equation with any… (More)
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2010
2010
Ranks of twists of elliptic curves and Hilbert's tenth problem
In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields… (More)
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2010
2010
HILBERT ' S TENTH PROBLEM FOR QUADRATIC RINGS
  • J. DENEFl
  • 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 determine… (More)
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2008
2008
Matrix Equations and Hilbert's Tenth Problem
We show a reduction of Hilbert’s tenth problem to the solvability of the matrix equation A1 1 A i2 2 · · ·A ik k = Z over non… (More)
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Review
2008
Review
2008
Elliptic Divisibility Sequences and Hilbert's Tenth Problem
Following ideas of Poonen, we use elliptic divisibility sequences to construct two subrings of the field of rational numbers… (More)
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2007
2007
Elliptic Curves and Hilbert's Tenth Problem
Following ideas of Poonen, we use elliptic divisibility sequences to construct two subrings of the field of rational numbers… (More)
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Review
2005
Review
2005
Hilbert's Tenth Problem and Paradigms of Computation
This is a survey of a century long history of interplay between Hilbert’s tenth problem (about solvability of Diophantine… (More)
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2004
2004
Hilbert's tenth problem for function fields of varieties over â„‚
Let K be the function field of a variety of dimension ≥ 2 over an algebraically closed field of characteristic zero. Then Hilbert… (More)
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2003
2003
On the bounded version of Hilbert's tenth problem
ABSTRACT Hilbert's Tenth problem on erned the de idability of Diophantine equations over the integers. Its negative solution, the… (More)
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2003
2003
Numerical simulations of a quantum algorithm for Hilbert's tenth problem
We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert’s… (More)
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1992
1992
Hilbert's tenth problem is of unification type zero
We show that the problem of finding integer solutions to a polynomial equation over the integers has unification type zero, i.e… (More)
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