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Abstract: Let F be a function field of characteristic p>2, finitely generated over a field C algebraic over a finite field Cp and such that it has an extension of degree p. Then Hilbert's Tenth Problem is not decidable over F . 1 (Update)
Context of citations to this paper: More
...extended Pheidas results to other function fields over fields of constants of characteristic greater than 2. See [26] 30] and [22]) Beyond the fact that Diophantine undecidability of many function fields of positive characteristic has been established, a p adic...
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BibTeX entry: (Update)
Alexandra Shlapentokh. Diophantine undecidability of function fields of characteristic greater than 2, finitely generated over fields algebraic over a finite field. Pre-print. http://citeseer.ist.psu.edu/article/shlapentokh01diophantine.html More
@misc{ shlapentokh-diophantine,
author = "A. Shlapentokh",
title = "Diophantine undecidability of function fields of characteristic greater
than",
text = "Alexandra Shlapentokh. Diophantine undecidability of function fields of
characteristic greater than 2, finitely generated over fields algebraic
over a finite field. Pre-print.",
url = "citeseer.ist.psu.edu/article/shlapentokh01diophantine.html" }
Citations (may not include all citations):59 Algebraic Number Theory (context) - Lang - 1970
47 Algebraic Number Theory (context) - Cassels, Frolich - 1967
37 Basic Number Theory (context) - Weil - 1974
30 Field Arithmetic (context) - Fried, Jarden - 1986
27 Hilbert's tenth problem is unsolvable (context) - Davis - 1973
14 Introduction to the theory of Algebraic Functions of One Var.. (context) - Chevalley - 1951
8 The topology of rational points - Mazur - 1992
6 Hilbert's tenth problem for a class of rings of algebraic in.. (context) - Pheidas - 1988
6 Diophantine sets over some rings of algebraic integers (context) - Denef, Lipshitz - 1978
5 Transactions of American Mathematical Society (context) - Denef, of - 1980
5 Hilbert's tenth problem for fields of rational functions ove.. (context) - Pheidas - 1991
5 Extension of Hilbert's tenth problem to some algebraic numbe.. (context) - Shlapentokh - 1989
5 Double fibres and double covers: Paucity of rational points (context) - Colliot-Thelene, Skorobogatov et al. - 1997
5 Questions of decidability and undecidability in number theor.. (context) - Mazur - 1994
4 Hilbert's tenth problem for algebraic function fields over i.. (context) - Shlapentokh - 2000
4 Hilbert's tenth problem for rational function fields in char.. (context) - Videla - 1994
4 Diophantine relations between algebraic number fields (context) - Shapiro, Shlapentokh - 1989
4 Diophantine undecidability of C (context) - Kim, Roush - 1992
4 Positive aspects of a negative solution (context) - Davis, Matijasevich et al. - 1976
4 Hilbert's tenth problem for quadratic rings (context) - Denef - 1975
4 Speculation about the topology of rational points: An up-dat.. (context) - Mazur - 1995
4 Diophantine definability over some rings of algebraic number.. (context) - Shlapentokh - 1997
4 Defining integrality at prime sets of high density in number.. (context) - Shlapentokh - 2000
3 The diophantine problem for polynomial rings and fields of r.. (context) - Denef - 1978
2 Diophantine unsolvability over p-adic function fields (context) - Kim, Roush - 1995
2 Diophantine unsolvability for function fields over certain i.. (context) - Kim, Roush - 1992
2 Diophantine undecidability in some rings of algebraic number.. (context) - Shlapentokh - 1994
2 Topology of diophantine sets: Remarks on Mazur's conjectures (context) - Cornelissen, Zahidi - 2000
2 Diophantine undecidability of algebraic function fields over.. (context) - Shlapentokh - 1996
2 Open problems regarding rational points on curves and variet.. (context) - Mazur - 1998
2 The existential theory of real hyperelliptic fields (context) - Zahidi - 2000
1 Gordon Breach Science Publishers (context) - Artin, Algebraic - 1986
1 Defining constant polynomials (context) - Prunescu - 2000
Documents on the same site (http://www.math.ecu.edu/~shlapent/): More
On Diophantine definability and decidability in large subrings.. - Shlapentokh (2001) (Correct)
On Diophantine definability and decidability in some infinite.. - Shlapentokh (2001) (Correct)
Defining Integrality at Prime Sets of High Density over.. - Shlapentokh (2001) (Correct)
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