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)
Wikipedia

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2010
2010
In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields… (More)
Is this relevant?
2010
2010
  • 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)
Is this relevant?
2008
2008
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)
Is this relevant?
Review
2008
Review
2008
Following ideas of Poonen, we use elliptic divisibility sequences to construct two subrings of the field of rational numbers… (More)
Is this relevant?
2007
2007
Following ideas of Poonen, we use elliptic divisibility sequences to construct two subrings of the field of rational numbers… (More)
Is this relevant?
Review
2005
Review
2005
This is a survey of a century long history of interplay between Hilbert’s tenth problem (about solvability of Diophantine… (More)
Is this relevant?
2004
2004
Let K be the function field of a variety of dimension ≥ 2 over an algebraically closed field of characteristic zero. Then Hilbert… (More)
Is this relevant?
2003
2003
ABSTRACT Hilbert's Tenth problem on erned the de idability of Diophantine equations over the integers. Its negative solution, the… (More)
Is this relevant?
2003
2003
We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert’s… (More)
  • figure 1
  • figure 2
  • figure 3
  • figure 4
  • figure 5
Is this relevant?
1992
1992
We show that the problem of finding integer solutions to a polynomial equation over the integers has unification type zero, i.e… (More)
Is this relevant?