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Author Shlapentokh, Alexandra.

Title Hilbert's tenth problem : diophantine classes and extensions to global fields / Alexandra Shlapentokh
Published Cambridge, UK ; New York : Cambridge University Press, 2006
Online access available from:
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Description 1 online resource (xiii, 320 pages)
Series New mathematical monographs ; 7
New mathematical monographs ; 7
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
Bibliography Includes bibliographical references (pages 310-316) and index
Notes Print version record
Subject Algebraic number theory.
Diophantine equations.
Hilbert's tenth problem.
Form Electronic book
ISBN 0511255810 (ebook ; ebrary)
0511256906 (electronic bk.)
0511257406 (electronic bk.)
051154295X (electronic book)
0521833604 (hbk.)
9780511255816 (ebook ; ebrary)
9780511256905 (electronic bk.)
9780511257407 (electronic bk.)
9780511542954 (electronic book)
9780521833608 (hbk.)
Other Titles Diophantine classes and extensions to global fields