Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1967

Preprint Number 1967

Previous Next Preprint server

1967. William Gasarch
Hilbert's Tenth Problem: Refinements and Variants

Submission date: 15 April 2021


Hilbert's 10th problem, stated in modern terms, is: Find an algorithm that will, given p in ℤ[x_1,...,x_n] determine if there exists a_1, a_2, ..., a_n in ℤ such that p(a_1,...,a_n)=0. Davis, Putnam, Robinson, and Matijasevic showed that there is no such algorithm. We look at what happens (1) for fixed degree and number of variables, (2) for particular equations, and (3) for variants which reduce the number of variables needed for undecidability results.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2104.07220: pdf, ps.

Last updated: April 20 2021 14:31 Please send your corrections to: