Hilbertʼs tenth problem for rational function fields over padic fields
 Author
 Claudia Degroote (UGent) and Jeroen Demeyer (UGent)
 Organization
 Abstract
 Let K be a padic field (a finite extension of some Q_p) and let K(t) be the field of rational functions over K. We define a kind of quadratic reciprocity symbol for polynomials over K and apply it to prove isotropy for a certain class of quadratic forms over K(t). Using this result, we give an existential definition for the predicate “v_t(x) >= 0” in K(t). This implies undecidability of diophantine equations over K(t).
 Keywords
 Undecidability, Hilbert's Tenth Problem, Quadratic form, Valuation, Diophantine set
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU4128132
 MLA
 Degroote, Claudia, and Jeroen Demeyer. “Hilbertʼs Tenth Problem for Rational Function Fields over Padic Fields.” JOURNAL OF ALGEBRA 361 (2012): 172–187. Print.
 APA
 Degroote, C., & Demeyer, J. (2012). Hilbertʼs tenth problem for rational function fields over padic fields. JOURNAL OF ALGEBRA, 361, 172–187.
 Chicago authordate
 Degroote, Claudia, and Jeroen Demeyer. 2012. “Hilbertʼs Tenth Problem for Rational Function Fields over Padic Fields.” Journal of Algebra 361: 172–187.
 Chicago authordate (all authors)
 Degroote, Claudia, and Jeroen Demeyer. 2012. “Hilbertʼs Tenth Problem for Rational Function Fields over Padic Fields.” Journal of Algebra 361: 172–187.
 Vancouver
 1.Degroote C, Demeyer J. Hilbertʼs tenth problem for rational function fields over padic fields. JOURNAL OF ALGEBRA. 2012;361:172–87.
 IEEE
 [1]C. Degroote and J. Demeyer, “Hilbertʼs tenth problem for rational function fields over padic fields,” JOURNAL OF ALGEBRA, vol. 361, pp. 172–187, 2012.
@article{4128132, abstract = {Let K be a padic field (a finite extension of some Q_p) and let K(t) be the field of rational functions over K. We define a kind of quadratic reciprocity symbol for polynomials over K and apply it to prove isotropy for a certain class of quadratic forms over K(t). Using this result, we give an existential definition for the predicate “v_t(x) >= 0” in K(t). This implies undecidability of diophantine equations over K(t).}, author = {Degroote, Claudia and Demeyer, Jeroen}, issn = {00218693}, journal = {JOURNAL OF ALGEBRA}, keywords = {Undecidability,Hilbert's Tenth Problem,Quadratic form,Valuation,Diophantine set}, language = {eng}, pages = {172187}, title = {Hilbertʼs tenth problem for rational function fields over padic fields}, url = {http://dx.doi.org/10.1016/j.jalgebra.2012.03.039}, volume = {361}, year = {2012}, }
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