| Description |
1 online resource (xiii, 320 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
New mathematical monographs ; 7
|
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New mathematical monographs ; 7.
|
| Bibliography |
Includes bibliographical references (pages 310-316) and index. |
| Contents |
Introduction -- Diophantine classes: definitions and basic facts -- Diophantine equivalence and Diophantine decidability -- Integrality at finitely many primes and divisibility of order at infinitely many primes -- Bound equations for number fields and their consequences -- Units of rings of W-integers of norm 1 -- Diophantine classes over number fields -- Diophantine undecidability of function fields -- Bounds for function fields -- Diophantine classes over function fields -- Mazur's conjectures and their consequences -- Results of Poonen -- Beyond global fields -- Recursion (computability) theory -- Number theory. |
| Summary |
Hilbert's Tenth Problem - to find an algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions - was shown to be unsolvable in the late sixties. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Hilbert's tenth problem.
|
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Hilbert's tenth problem. |
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Algebraic number theory.
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Algebraic number theory. |
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Diophantine equations.
|
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Diophantine equations. |
| Genre/Form |
Electronic books.
|
| Added Title |
Diophantine classes and extensions to global fields |
| Other Form: |
Print version: Shlapentokh, Alexandra. Hilbert's tenth problem. Cambridge, UK ; New York : Cambridge University Press, 2006 0521833604 9780521833608 (DLC) 2007360684 (OCoLC)75713026 |
| ISBN |
9780511257407 (electronic book) |
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0511257406 (electronic book) |
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0521833604 (hardback) |
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9780521833608 (hardback) |
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0511255810 (ebook ; ebrary) |
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9780511255816 (ebook ; ebrary) |
|
0511256906 (electronic book) |
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9780511256905 (electronic book) |
|
0511256388 |
|
9780511256387 |
|
051154295X (electronic book) |
|
9780511542954 (electronic book) |
|
