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MR1802010 03B25 (03D35 11U05)
Shlapentokh, Alexandra Hilbert's tenth problem over number fields, a survey. Hilbert's tenth problem: relations with arithmetic and algebraic geometry (Ghent, 1999), 107–137, Contemp. Math., 270, Amer. Math. Soc., Providence, RI, 2000.
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