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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
正題名/作者:	Hilbert's tenth problem :/ Alexandra Shlapentokh.
其他題名:	diophantine classes and extensions to global fields /
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:	Diophantine equations. -
電子資源:	https://doi.org/10.1017/CBO9780511542954
ISBN:	9780511542954 (ebook)

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 ;31..

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:

792270
Diophantine equations.

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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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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 Diophantine equations. $3 792270
650 0 $a Algebraic number theory. $3 672442
650 0 $a Hilbert's tenth problem. $3 1443363
776 0 8 $i Print version: $z 9780521833608
830 0 $a New mathematical monographs ; $v 31. $3 1238333
856 4 0 $u https://doi.org/10.1017/CBO9780511542954