Ten unknowns for Hilbert's tenth problem over the integers
Zhi-Wei Sun
Abstract
Hilbert's Tenth Problem over the integers was solved negatively by Y. Matiyasevich in 1970. In this paper, we prove that there is no algorithm to determine for any polynomial equation P(z1,…,z10)=0 (with integer coefficients and ten unknowns) whether it has integer solutions. This improves the previous 11 unknowns theorem.
Create a lesson
Related papers
A new proof that more than 2/3 of the zeros of the Riemann zeta function are simple and on the critical line
Youness Lamzouri
Petersson-Rigid Lattices in a Census of 100 Rank-Three Root Bases
Eungang Cho
Adelic points and unmramified Brauer approximation for classifying stacks
Ajneet Dhillon
On divergence related to Riemann--von Mangoldt's explicit formula of the prime-counting function
Harald Grobner
On the occurrence of congruence multiplicities between Ramanujan's theta functions
Shane Chern, Nicolas Allen Smoot, Dazhao Tang
Improved Weyl bounds on short intervals
Xiyu Hu