Advanced search
2 files | 513.49 KB Add to list

Diophantine sets of polynomials over algebraic extensions of the rationals

Claudia Degroote (UGent) and Jeroen Demeyer (UGent)
(2014) JOURNAL OF SYMBOLIC LOGIC. 79(3). p.733-747
Author
Organization
Abstract
Let L be a recursive algebraic extension of Q. Assume that, given alpha is an element of L, we can compute the roots in L of its minimal polynomial over Q and we can determine which roots are Aut(L)-conjugate to alpha. We prove that there exists a pair of polynomials that characterizes the Aut(L)-conjugates of alpha, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in R, or in a finite extension of Q(p) (with p an odd prime). Then we show that subsets of L[X](k) that are recursively enumerable for every recursive presentation of L[X], are diophantine over L[X].
Keywords
FUNCTION-FIELDS, HILBERTS 10TH PROBLEM, diophantine sets, Hilbert's tenth problem, recursively enumerable sets

Downloads

  • qalgpoly.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 149.14 KB
  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 364.35 KB

Citation

Please use this url to cite or link to this publication:

MLA
Degroote, Claudia, and Jeroen Demeyer. “Diophantine Sets of Polynomials over Algebraic Extensions of the Rationals.” JOURNAL OF SYMBOLIC LOGIC 79.3 (2014): 733–747. Print.
APA
Degroote, C., & Demeyer, J. (2014). Diophantine sets of polynomials over algebraic extensions of the rationals. JOURNAL OF SYMBOLIC LOGIC, 79(3), 733–747.
Chicago author-date
Degroote, Claudia, and Jeroen Demeyer. 2014. “Diophantine Sets of Polynomials over Algebraic Extensions of the Rationals.” Journal of Symbolic Logic 79 (3): 733–747.
Chicago author-date (all authors)
Degroote, Claudia, and Jeroen Demeyer. 2014. “Diophantine Sets of Polynomials over Algebraic Extensions of the Rationals.” Journal of Symbolic Logic 79 (3): 733–747.
Vancouver
1.
Degroote C, Demeyer J. Diophantine sets of polynomials over algebraic extensions of the rationals. JOURNAL OF SYMBOLIC LOGIC. 2014;79(3):733–47.
IEEE
[1]
C. Degroote and J. Demeyer, “Diophantine sets of polynomials over algebraic extensions of the rationals,” JOURNAL OF SYMBOLIC LOGIC, vol. 79, no. 3, pp. 733–747, 2014.
@article{4128161,
  abstract     = {Let L be a recursive algebraic extension of Q. Assume that, given alpha is an element of L, we can compute the roots in L of its minimal polynomial over Q and we can determine which roots are Aut(L)-conjugate to alpha. We prove that there exists a pair of polynomials that characterizes the Aut(L)-conjugates of alpha, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in R, or in a finite extension of Q(p) (with p an odd prime). Then we show that subsets of L[X](k) that are recursively enumerable for every recursive presentation of L[X], are diophantine over L[X].},
  author       = {Degroote, Claudia and Demeyer, Jeroen},
  issn         = {0022-4812},
  journal      = {JOURNAL OF SYMBOLIC LOGIC},
  keywords     = {FUNCTION-FIELDS,HILBERTS 10TH PROBLEM,diophantine sets,Hilbert's tenth problem,recursively enumerable sets},
  language     = {eng},
  number       = {3},
  pages        = {733--747},
  title        = {Diophantine sets of polynomials over algebraic extensions of the rationals},
  url          = {http://dx.doi.org/10.1017/jsl.2013.9},
  volume       = {79},
  year         = {2014},
}

Altmetric
View in Altmetric
Web of Science
Times cited: