Book Review: Hilbert\RM 's Tenth Problem
نویسندگان
چکیده
منابع مشابه
Divisibility Sequences and Hilbert ’ S Tenth Problem Graham
Following ideas of Poonen, we use elliptic divisibility sequences to construct two subrings of the field of rational numbers, which generate the field, and for which Hilbert's Tenth Problem is undecidable. In 1970, Matijasevi˘ c [19], building upon earlier work of Davies, Put-nam and Robinson [6], resolved negatively Hilbert's Tenth Problem for the ring Z, of rational integers. This means there...
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Following ideas of Poonen, we use elliptic divisibility sequences to construct two subrings of the field of rational numbers , whose compositum is the field, and for which Hilbert's Tenth Problem is undecidable. In 1970, Matijasevic [17], building upon earlier work of Davies, Put-nam and Robinson [5], resolved negatively Hilbert's Tenth Problem (hereafter Hilbert10) for the ring Z, of rational ...
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Descent via an isogeny on an elliptic curve is used to construct two subrings of the field of rational numbers, which are complementary in a strong sense, and for which Hilbert's Tenth Problem is undecidable. This method further develops that of Poonen, who used elliptic divisibility sequences to obtain undecid-ability results for some large subrings of the rational numbers. In 1970, Matijasevi...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1995
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1995-00546-x