James P. Jones

Publications29
h-index12
Citations492
Highly Influential Citations31
Claim Author Page
Author pages are created from data sourced from our academic publisher partnerships and public sources.

Recommended Authors

  • Martin D. Davis
  • 164 Publications • 9,885 Citations
  • L. Dries
  • 152 Publications • 4,902 Citations
  • Y. Matiyasevich
  • 117 Publications • 1,229 Citations
  • H. Putnam
  • 440 Publications • 26,729 Citations
  • Publications
  • Influence
Universal Diophantine Equation
TLDR
Matijasevic's theorem implies the existence of a diophantine equation U such that for all x and v, x ∈ W v is also recursively enumerable, and the nonexistence of such an algorithm follows immediately from theexistence of r.e. nonrecursive sets.
View via Publisher
DIOPHANTINE REPRESENTATION OF THE SET OF PRIME NUMBERS
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and…
View via Publisher
Proof or recursive unsolvability of Hilbert's tenth problem
(1991). Proof of Recursive Unsolvability of Hilbert's Tenth Problem. The American Mathematical Monthly: Vol. 98, No. 8, pp. 689-709.
View via Publisher
Undecidable diophantine equations
In 1900 Hubert asked for an algorithm to decide the solvability of all diophantine equations, P(x1, . . . , xv) = 0, where P is a polynomial with integer coefficients. In special cases of Hilbert's…
View via Publisher
Register Machine Proof of the Theorem on Exponential Diophantine Representation of Enumerable Sets
TLDR
A new, simple proof of the theorem of M. Davis, Putnam and Robinson, which states that every recursively enumerable relation A is exponential diophantine, is given, where a 1 …, a n, x 1 , …, x m range over natural numbers and R and S are functions built up from these variables and natural number constants.
View via Publisher
Classification of Quantifier Prefixes Over Diophantine Equations
View via Publisher
Variants of Robinson's essentially undecidable theoryR
TLDR
An essentially undecidable theory based on three axiom schemes involving only multiplication and less than or equals is given.
View on Springer
Formula for the Nth Prime Number
In this note we give a simple formula for the nth prime number. Let pn denote the nth prime number (p 1=2, p 2 = 3, etc.). We shall show that p n is given by the following formula.
View on Cambridge Press
Diophantine representation of Mersenne and Fermat primes
View via Publisher
Recursive Undecidability — An Exposition
View via Publisher
...
...