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EBOOK
Author Shlapentokh, Alexandra.
Title Hilbert's tenth problem : diophantine classes and extensions to global fields / Alexandra Shlapentokh.
Imprint Cambridge, UK ; New York : Cambridge University Press, 2006.

Author Shlapentokh, Alexandra.
Series New mathematical monographs ; 7.
New mathematical monographs ; 7.
Subject Hilbert's tenth problem.
Algebraic number theory.
Diophantine equations.
Add Title Diophantine classes and extensions to global fields
Author Shlapentokh, Alexandra.
Series New mathematical monographs ; 7.
New mathematical monographs ; 7.
Subject Hilbert's tenth problem.
Algebraic number theory.
Diophantine equations.
Add Title Diophantine classes and extensions to global fields
Description 1 online resource (xiii, 320 pages).
polychrome rdacc
Bibliography Note 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.
Note Print version record.
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.
ISBN 9780511257407 (electronic bk.)
0511257406 (electronic bk.)
0521833604 (hbk.)
9780521833608 (hbk.)
0511255810 (ebook ; ebrary)
9780511255816 (ebook ; ebrary)
0511256906 (electronic bk.)
9780511256905 (electronic bk.)
0511256388
9780511256387
051154295X (electronic book)
9780511542954 (electronic book)
OCLC # 159933215
Additional Format Print version: Shlapentokh, Alexandra. Hilbert's tenth problem. Cambridge, UK ; New York : Cambridge University Press, 2006 0521833604 9780521833608 (DLC) 2007360684 (OCoLC)75713026.


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