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Hilbert's tenth problem :diophantine classes and extensions to global fields /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	512.7
書名/作者:	Hilbert's tenth problem : : diophantine classes and extensions to global fields // Alexandra Shlapentokh.
作者:	Shlapentokh, Alexandra,
面頁冊數:	1 online resource (xiii, 320 pages) : : digital, PDF file(s).
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Hilbert's tenth problem.
標題:	Algebraic number theory.
標題:	Diophantine equations.
ISBN:	9780511542954 (ebook)
內容註:	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.
摘要、提要註:	In the late sixties Matiyasevich, building on the work of Davis, Putnam and Robinson, showed that there was no algorithm to determine whether a polynomial equation in several variables and with integer coefficients has integer solutions. Hilbert gave finding such an algorithm as problem number ten on a list he presented at an international congress of mathematicians in 1900. Thus the problem, which has become known as Hilbert's Tenth Problem, was shown to be unsolvable. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields including, in the function field case, the fields themselves. While written from the point of view of Algebraic Number Theory, the book includes chapters on Mazur's conjectures on topology of rational points and Poonen's elliptic curve method for constructing a Diophatine model of rational integers over a 'very large' subring of the field of rational numbers.
電子資源:	http://dx.doi.org/10.1017/CBO9780511542954

Hilbert's tenth problem :diophantine classes and extensions to global fields /
Shlapentokh, Alexandra,

Hilbert's tenth problem :diophantine classes and extensions to global fields /Alexandra Shlapentokh. - 1 online resource (xiii, 320 pages) :digital, PDF file(s). - New mathematical monographs ;7. - New mathematical monographs ;3..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

In the late sixties Matiyasevich, building on the work of Davis, Putnam and Robinson, showed that there was no algorithm to determine whether a polynomial equation in several variables and with integer coefficients has integer solutions. Hilbert gave finding such an algorithm as problem number ten on a list he presented at an international congress of mathematicians in 1900. Thus the problem, which has become known as Hilbert's Tenth Problem, was shown to be unsolvable. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields including, in the function field case, the fields themselves. While written from the point of view of Algebraic Number Theory, the book includes chapters on Mazur's conjectures on topology of rational points and Poonen's elliptic curve method for constructing a Diophatine model of rational integers over a 'very large' subring of the field of rational numbers.

ISBN: 9780511542954 (ebook)Subjects--Topical Terms:

643499
Hilbert's tenth problem.

LC Class. No.: QA242 / .S53 2007

Dewey Class. No.: 512.7

Hilbert's tenth problem :diophantine classes and extensions to global fields /
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505 0 $a 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.
520 $a In the late sixties Matiyasevich, building on the work of Davis, Putnam and Robinson, showed that there was no algorithm to determine whether a polynomial equation in several variables and with integer coefficients has integer solutions. Hilbert gave finding such an algorithm as problem number ten on a list he presented at an international congress of mathematicians in 1900. Thus the problem, which has become known as Hilbert's Tenth Problem, was shown to be unsolvable. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields including, in the function field case, the fields themselves. While written from the point of view of Algebraic Number Theory, the book includes chapters on Mazur's conjectures on topology of rational points and Poonen's elliptic curve method for constructing a Diophatine model of rational integers over a 'very large' subring of the field of rational numbers.
650 0 $a Hilbert's tenth problem. $3 643499
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